PROBABILITY (Basic)

          .     PROBABILITY
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1)A coin is tossed once. Find the probability of getting head

2) A dice is thrown once. What is the probability of getting a prime number.

3)a) A die is thrown once. What is the probability of getting a number other than 4 ?

b) A ‘3’

c) A ‘4’

c) An odd number

d) A Number greater than 4

4) Three unbiased coins are tossed simultaneously. Find the probability of getting

a) All heads

b) All tails

c) No head.

d) No tail

e) Atleast one head

f) Atleast one tail

g) All not heads

h) Atmost one tail

I) Two or more tails

j) More than two tails

k) Less than one head

l) Heads and tails

m) Heads are the two extremes

n) Heads will come in the 1st row

o) Heads will exceed the number of tails in a particular throw.

p) Exactly 2 heads

q) Atmost two heads.

r) Atleast two heads

5) Two coins are tossed simultaneously. What is the probability
a)All heads

b) All tails

c) No heads

d) No tails

e) All not heads

f) at least one head

g) Exactly one head

h) At Most one head.

i) Atleast two heads

j) Heads will come in first row.

k) Heads and tails will occur alternately.

6) One card is drawn at random from well shuffled pack of cards. What is the probability of
drawing a

a) A King.

b) A queen

c) An eight

d) A black card

e) The six of the clubs.

f) A spade.

g) A King of red suit

h) A queen of black suit

i) A pack of hearts.

j) A red of face’card.

k) A King or a jack

l) A non-Ace

m) A red card

n) Neither king nor a queen

o) Neither a red card nor a queen.

p) It is either a King or a knave

q) It is neither a King nor a Knave

r) It is neither a heart nor a diamond

s) It is neither an Ace, nor a King, nor a Queen, nor a Knave.

t) A spade or an Ace not of a spade.

7) Two dice are rolled simultaneously. What is the probability of getting

a) 8 as the sum of two numbers that turn up

b) A doublet

c) Sum is 7

d) Sum is 11

e) It is either 7 or 11.

f) It is neither 7 nor 11.

g) Sum is odd number more
     than 3.

h) Sum is a multiple of 4.

i) Sum is a multiple of 3 and 4

j) Sum is multiple of 3 or 4.

k) Sum is atleast 8

l) Sum is Atmost 7

m) The product of the faces is 12.

n) Sum of the faces is more
     than 12

8) There are 35 students in a class of whom 20 are boys and 15 are girls. From these students one is chosen at random. What is the probability that the chosen student is a

a) A Boy

b) A girl.

9) Seventeen cards numbered 1,2,3...16,17 are put in a box and mix thoroughly. One person draw a card from the box. Find probability that the number on the card is

a)A prime

b) Divisible by 3

c) Divisible by 2 and 3 both

d) Not divisible by 2

e) Divisible by 2 but not by 3

f) Divisible by 3 but not by 2

g) Divisible by either 3 or 2

h) Neither Divisible by 2 nor 3

i) multiple of 4

10) A bag contains 6 Red,8 white balls, 5 green and 3 black balls . One ball is drawn at random from the bag. Find the probability that the ball is:

a) White

b) Red or White

c) Not green

d) Neither white nor black

e) A pink ball

11) From a pack of cards jacks, queens,kings and aces of red colours are removed. From the remaining, a card is drawn random. Find the probability:

a)A black queen

b) A red card

c) A picture card

12) The probability that will rain today is 0.84. what is the probability that will not rain today ?

13) What is the probability that an ordinary year has 53 Sundays

14) Find the probability of getting 53 Friday in a leap year

15) In a lottery there are 10 prizes and 25 blanks . What is the probability of getting a prize ?

16) It is known that a box of 200 electric bulbs contains 16 defective bulbs. One bulb is taken out random from the box. What is the probability that the bulb drawn is

a) Defective

b) not defective.

17) A bag contains 3 green and 8 white balls. If one ball is drawn at random. Find the probability that:

a)It is green

b) It is white

18) There are 17 numbered 1 to 17 in a bag, If a person selects one ball is drawn randomly. Find the probability that the number printed on the ball will be an even number greater than 9.

19)An urn contains 9 balls, 2 of which are white, 3 blue and 4 black. 3 balls are drawn at random from the urn. What is the probability that
a) balls are different colours

b) 2 balls will be the same colour.

c) three balls will be the same colour.

d) All are black.

e) 2 blue balls.

f) 2 black 1 white.

g) black is more than other.

g) Consecutive colour.

h) No black

i) Neither white nor blue.

j) Atleast one white

k) Atleast one black

l) Atleast one blue

m) Atmost one blue

n) Atmost one black.

20) One card is drawn from a pack of cards. Find the probability that

a)Either a spade or a diamond

b) Either a spade or a king.

c) Neither king nor diamond.

d) Either red or queen.

21) Out of the number 1 to 120, one is selected at random. What is the probability that it is divisible by
a)10 or 13
b) 8 or 10

22) One counter is drawn at random from a bag contain 70 counters marked with the first 70 numerical. Find the chance that:
a) multiple of 8 or 9
b) either multiple of 3 or 4

23) A bag contains 10 red and 6 green balls. Two successive drawings of three balls are made (i) with (ii) without replacement
a) first drawing will give 3 red balls and second will give 3 green balls.

24) A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. Find the probability that:
a)Two tails
b) head and Number 6
c) head and an even number.

25) Four cards are drawn from a pack of cards. Find the probability
a)All the 4 cards of the same suit
b) all 4 cards of the same number
c) one card from each suite
d) two red and two black cards.
e) all cards of the same colour
f) All face cards.

26) A box contains 10 bulbs, of which just 3 are defective. If a random of 5 bulbs is drawn find the probability that:
a) Exactly one defective bulb
b) exactly two defective bulbs
c) no defective bulbs.

27) 5 marbles are drawn from a bag which contains 7 blue and 4 black marbles. Find probability
a)All will be blue
b) 3 will be blue and 2 black.

28) Find the probability that when a hand of 7 cards is dealt from a pack of cards
a)All kings
b) exactly 3 kings
c) atleast 3 kings.

29) What is the probability that in a group of 3 people
a) 3 people having same Birthday
b) 2 people have same birthday
c) All have different birthdays
d) atleast one have same birthday
e) Atleast 2 have same birthday
f) Atmost 2 have same birthday.

30) A fair coin with 1 marked on one face and 6 on the other and a fair dice are both tossed, find probability that the sum of Numbers a) 3.  b) 12

31) Five cards are drawn from a pack of 52 cards. What is the probability that:
a)Just one Ace
b) atleast one Ace

32) the face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random.find probability that they belong to different suits?

33) The Odd in favour of an event are 3:5. Find the probability of occurrence of this event.

34) If odd against an event be 7:9, find the probability of non-occurance of this event.

35) Two dice are thrown. Find the odds in favour of getting the sum
a) 4.   b) 5

36) What are the odds in favour of getting a spade if the card drawn from a pack of cards? What are the odds in favour of getting a king

37) If a letter is chosen at random from the English alphabet, find the probability that:
a)A vowel
b) A consonant

38) A class consists of 10 boys and 8 girls. Three students are selected at random. Find probability that the selected group
a)All boys
b) all girls
c) 1 boy and 2 girls
d) atleast one girl
e) Atmost one girl.

39) A four digited Number is formed by the digits 1,2,3,4 with no repetition. Find the probability that the number is
(a) odd
(b) Divisible by 4

40) A five digited Number is formed by the digits 0,1,2,3,4 with no repetition. Find the probability that the number is
(a) odd
b) Divisible by 4

41) The letter 'SUNDAY' are arranged at random. Find the probability that there will
a) begin with S
b) begin with S but not end with Y
c) the vowels will occupy odd places.
d) Vowels will be always together.

42) From 8 counters 1,2,.....8. four counters are selected at random. Find the probability of getting atleast one odd and one even counter.

43) A sub-committee of 6 members to be formed from 7 men and 4 ladies. Find the probability
a) Exactly two ladies.
b) atleast two ladies.

44) A bag contains 5 white and 4 black balls. One ball is drawn from the bag and replaced and then a second draw of a ball is made. What is the probability that the two balls drawn are
a)Same colours
b) Different colours
c) Both white
d) no white

45) A box contains 8 red and 5 white balls. Two successive drawings of 3 balls are made. Find the probability that the first drawing will give 3 white and the second 3 red balls. if the balls are drawn
(i) with replacement
(ii) without replacement.

46) Each of two identical bags contains 5 white and 5 red balls. One ball is transferred at random from the 2nd bag to the 1st and then one ball is drawn from the 1st bag. Find the probability that the ball drawn is red.

47) Boxes I and II contain 4 white, 3 red and 3 blue balls; and 5 white, 4 red and 3 blue balls. If one ball is drawn at random from each box, what is the probability that both balls are of the same colour ?

48) Two boxes contain respectively 4 white and 3 red balls; and 3 white and 7 red balls. A box is chosen at random and a ball is drawn from it. Find the probability that the ball is white.

49) An urn contains 5 white and 3 black balls; and a 2nd urn contains 4 white and 5 black balls. One of the urns is chosen at random and 2 balls are drawn from it. Find the probability that one is white and the other is black.

50) The odds against a certain events are 5:2 and the odds in favour of another event, independent of the former are 6:5. Find the chance that atleast one of the events will happen.

51) A speaks truth in 75% and B in 89% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact ?

52) A person is known to hit 4 out of 5 shots, whereas another person is known to hit 3 out of 4 shots. Find the probability of hitting a target if they both try.

53) A can solve 80% of the problems of Math and B can solve 70%. A problem is selected at random. What is the probability
a) exactly one of them solved
b) atleast one of them solved
c) Atmost one of them solved
d) no one solved

54) The probability that a student passes in Math test is 2/3 and the probability that he passes both maths and stats test is 14/45. The probability that he passes atleast one test is 4/5. What is the probability that he passes the stats test.

55) Mr. X is called for interview for 3 separate posts. At the first interview there are 5 candidates, at the 2nd 4 candidates and at the 3rd 3 candidates. If the selection of each item is equally likely, find the probability that Mr. X will be selected for atleast one post.

56) A problem of Maths is given to A,B and C whose chances of solving it are 1/3,1/4,1/5 respectively. Find the probability
a) all of them solved
b) no one solved
c) Exactly one of them solved
d) Exactly two of them solved
e) atleast one of them solved
f) Atmost one of them solved
g) Maths will be solved.

57) In a given race the odd in favour of four horces A,B,C,D are 1:3,1:4,1:5,1:6 respectively. Assuming that a dead heat is impossible, find the probability that one of them wins the race.

58) A, B in that order toss a coin. The first one to throws head wins. What are their respective chances of winning? Assume that the game may continue indefinitely.

59)A, B ,C in that order toss a coin. The first one to throws head wins. What are their respective chances of winning? Assume that the game may continue indefinitely.

60)(I) If A and B are mutually exclusive events and P(A)=½, P(B)=⅓, then find the value of P(A+B).

ii) If P(A)=¼, P(B)=⅔ and P(A+B)=½ find P(AB).

iii) P(A)=0.4, P(B)=0.8 and
    P(B/A)=0.6  find P(AB)
     and P(A/B).

iv) P(A)=0.5, P(B)=0.6
     and P(A+B)=0.8 find
     P(AB),P(A/B),P(B/A)

(v) P(A)= 2P(B)=3P(C), find
      P(A), P(B), P(C).

61) i) If the events A and B are
independent to each other and
P(A)=0.3, P(B)=0.6, find the values of P(AB) and P(A+B)

62) i) P(A)=0.42, P(B)=0.48 and P(AB)=0.16 find the values of P(A)' , P(B)' , and (A+B)'

ii) The events A,B,C are independent to each other and P(A)= ⅓ , P(B)=⅔ P(C)=3/4 find P(A+B+C).

63) If P(A)= 1/2, P(B)= 1/3,
P(AB)= 1/4 then find
P(A+B), P(A/B), P(A' . B'),  P(A'+B'),
P(A' .B)

64) If the events A and B are
independent to each other and
P(A+B)=0.6, P(A)=0.2, find P(B)

65) P(A')=0.7, P(B)=0.7, P(B/A)=0.5 find P(A/B),and P(A+B)

66) If A,B,C are independent to each otherP(A)=1/2, P(B)=1/3, P(C)=¼ find P(A+B+C).

67) P(A)=1/2, P(A)=3/5, P(AB)=⅓
P(A+B), P(A'B'), P(A' + B'),  P(AB'),
P(A' .B) .

68) P(A)=1/4, P(B)=2)5, P(A+B)=1/2,  Find the values of P(AB), P(AB'), P(A' + B'),

69) P(A)=2)3, P(B)= 1/2,
P(A' + B')=5/6 find the values of
P(A+B), P(AB), P(A/B), P(B/A),  P(AB'), P(A' .B') .

70) If A and B are mutually exclusive events and P(A)=0.3, P(B)=p and P(A+B)=0.6 find p.

71) if A and B are two independent events and P(A)=0.4, P(B)=p, P(A+B)=0.6, find the value of p.

72) If P(A)=⅜, P(B)=⅝,P(AB)=¼ find P(A/B), P(B/A).

73) If A and B are independent events and P(A)=⅗ P(B)=⅔, then find the value of P(A+B)

74) P(A)=1/4, P(B)=1/2,P(AB)=⅛ find P(A+B), P(A' . B').

75) If  P(A)= 0.3, P(B)=0.7,
P(B/A)=0.5 find P(A/B), P(A+B).

76)  P(A)=0.3, P(B)=0.7,P(B/A)=0.5
  find P(A/B), P(A+B).

77)  P(A/B)=⅖,  P(A)=⅓ and
P(B)=¼ , find P(B/A).

78) If A,B and C are mutually exclusive and exhaustive events and P (A)=3/5, P(B)=⅙ find P(C).