BASIC PROBABILITY -2
1) A bag contains 9 red, 7 white and 4 Black balls. If two balls are drawn at random, find the probability that;
A) both the balls are red. 18/95
B) one ball is is white. 91/190
C) the balls are of the same colour. 63/190
D) one is white and other red.
63/190
2) A box contains 10 red marbles , 20 blue Marbles 30 green Marbles. 5 Marbles are drawn from the box. what is the probability that
A) all will be blue. 34/11977
B) at least one will be green.
302/1121
3) A bag contains 50 tickets numbered 1,2, 3,..., 50 of which 5 are drawn at random and arranged in ascending order of magnitude (x₁ <x₂<x₃<x₄<x₅) Find the probability that x₃ = 30. 551/15134
4) 5 Marbles are drawn from a bag which contains 7 blue marbles and 4 Black marbles. What is the probability that
A) all will be blue ? 1/22
B) 3 will be blue and 2 black. 5/11
5) A box contains 10 bulbs, of which just three are defective. If a random sample of five bulbs is drawn, find the probabilities that the sample contains:
A) exactly one defective bulb. 5/12
B) exactly two defective bulbs. 5/12
C) no defective bulbs. 1/12
6) In a lottery of 50 tickets numbered 1 to 50, two tickets are drawn simultaneously. Find the probability that:
A) both the tickets drawn have prime numbers,. 21/245
B) none of the tickets drawn has prime number. 17/35
C) One ticket has prime number.
3/7
7) A bag contains tickets numbered 1 to 30. Three tickets are drawn at random from the bag. What is the probability that the maximum number of the selected tickets exceeds 25? 88/203
8) A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that one is white and one is blue. 4/17
9) a bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random. find the probability that
A) both balls are white. 7/40
B) one ball is black and the other red. 1/6.
C) both balls are of the same colour. 37/120
10) A bag contains 6 red, 4 white and 8 Blue Balls. If three balls are drawn at random, find the probability that:
A) 1 is red and 2 are white. 3/68
B) 2 are blue and 1 is red. 7/34
C) 1 is red. 33/68
11) A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that:
A) all 10 are defective. ²⁰C₁₀/¹⁰⁰C₁₀
B) all 10 are good ⁸⁰C₁₀/¹⁰⁰C₁₀
C) at least 1 is defective. 1 - ⁸⁰C₁₀₀/¹⁰⁰C₁₀
D) none is defective. ⁸⁰C₁₀/¹⁰⁰C₁₀
12) Two balls are drawn at random from a bag containing 2 white, 3 red, 5 green and 4 Black balls, one by one without replacement. Find the probability that both the balls are of different colours. 0.78
13) A bag contains 8 red, 3 white and 9 blue balls. if three balls are drawn at random, determine the probability that :
A) all the three balls are Blue Balls. 7/95
B) all the balls of different colour. 18/95
14) A bag contains 5 red, 6 white and 7 black balls, Two balls are drawn at random. What is the probability that both balls are red or both are black? 31/153
15) A box contains 10 red marbles. 20 blue Marbles and 30 green marbles . 5 marbles are drawn at random. From the box, what is the probability that:
A) all are blue. (²⁰C₅/⁴⁰C₀)/⁶⁰C₅
B) at least one green. 4367/4484
16) A box contains six red marbles numbered 1 through 6 and 4 white Marbles numbered from 12 through 15. find the probability that a marble drawn is
A) white 2/5
B) white and odd numbered. 1/5
C) even numbered. 1/2
D) red or even numbered. 4/5
17) A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that
A) both the tickets have prime numbers on them. 14/95
B) on one there is a prime number and on the other there is a multiple of 4. 4/19
18) An urn contains 7 white, 5 black and 3 red balls. two balls are drawn at random. find the probability that
A) both are balls are red. 1/35
B) one ball is red and the other is black. 1/7
C) one ball is is white. 8/15
19) In a lottery 10000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy
A) one ticket. 999/1000
B) 2 tickets. ⁹⁹⁹⁰C₂/¹⁰⁰⁰⁰C₂
C) 10 tickets. ⁹⁹⁹⁰C₁₀/ ¹⁰⁰⁰⁰C₁₀
20) Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting
A) all the four cards of the same suit. 198/20825
B) all the four cards of the same number. 13/270725
C) one card from each suit. 2197/20825
D) Two red cards and two black cards.. (²⁶C₂x²⁶C₂)/⁵²C₄
E) All cards cards of the same colour. 2(²⁶C₄)/⁵²C₄
F) All face cards. ¹²C₄/⁵²C₄
21) Find the probability that when a hand of 7 cards is dealt from a well shuffled deck of 52 cards, it contains.
A) all four Kings. 1/7735
B) exactly three kings. 9/1547
C) at least three kings. 46/7735
22) In shuffling a pack of 52 playing cards. four are accidentally dropped, find the chance that the missing cards should be one from each suit. 2197/20825.
23) From a deck of 52 cards, four cards are drawn simultaneously, find the chance that they will be the four Honours of the same suit. 2/5
24) Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain:
A) Just One ace. 3243/10829
B) at least one s 1 ace. 1000/9139
25) Two unbiased dice are thrown. find the probability that:
A) neither a doublet nor a total of 8 will appear. 13/18
B) the sum of the number obtained on the two dice is neither multiple of 2 nor a multiple of 3. 1/3
26) A fair coin with 1 marked on one face 6 on the other and a fair die are both tossed, find the probability that the sum of numbers that turns up is
A) 3 1/12
B)12 1/12
27) Five cards are drawn from a well shuffled pack of 52 cards. find the probability that all the five cards are hearts. 33/66640
28) The number lock of a suitcase has 4 wheels, each labelled with 10 digit i.e., from 0 to 9. The lock opens with a sequence of 4 digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase. 1/5040
29) Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope. 2/3
30) Out of 100 students, two sections of 40 and 60 students are formed. If you and your friends are among the 100 students, what is the probability that
A) you both enter the same section ? 17/33
B) you both enter the different sections ? 16/33
31) A word consists of 9 letters; 5 consonants and 4 vowels. Three letters are chosen at random. What is the probability that more than one vowel will be selected ? 17/42
32) Four person are to be chosen at random from a group of three men, 2 women and 4 children. Find the probability of selecting
A) 1 man, 1woman and 2 children
B) exactly 2 children
C) 2 woman. 2/7, 10/21, 1/6
33) 12 balls are distributed among three boxes, find the probability that the first box will contain 3 balls. (¹²C₃x 2⁹)/3¹²
34) Find the probability that birth days of six different persons will fall in exactly two calendar months. 341/12⁵
35) Find the probability that in a random arrangement of the letters of the word UNIVERSITY the two I's come together. 1/5
36) A five digit number is formed by the digits 1, 2, 3, 4, 5 without repetition. Find the probability that number is divisible by 4. 1/5
37) Out of 9 outstanding students in a college, there are 4 boys and 5 girls. A team of four students is to be selected for a quiz program program quiz programme. Find the probability that two are boys and two are girls. 10/21
38) In a lot of 12 microwave ovens, there are 3 defective units. A person has ordered 4 of these units and since each is identically packed, The selection will be random. What is is the probability that
A) all 4 units are good. 14/55
B) exactly 3 units are good. 28/55
C) At least two units are good. 54/55
39) There are 4 letters and 4 addressed envelopes. Find the probability that all the letters are not dispatched in a right envelopes. 23/24
40) The odds in favour of an event are 3:5. Find the probability of occurrence of this event. 3/8
41) In a relay race there are 5 teams A, B, C, D, E.
A) What is the probability that A, B and C finish first, second and third and third respectively. 1/60
B) What is the probability that A, B and C are first three to finish( in any order). 1/10
42) A card is drawn from an ordinary pack of 52 cards and a Gambler bets that, it is a spade or an Ace. What are the odds against his winning this bet. 9:4
43) find the probability that in a random arrangement of the letter of the word SUNDAY, viwels come together. 1/5
B) the letters of the word CLIFTON are placed at random in a row. What is the chance that two vowels come together? 2/7
44) the letter of the word FORTUNES are arranged at random in a row. What is the chance that the two T come together. 1/5
45) Find the probability that in a random arrangement of the letters of the word UNIVERSITY, the two I's do not come together. 4/5
46) If odds in favour of an event be 2:3, find the probability of occurrence of this event. 2/5
47) If odds against an event be 7:9, find the probability of non-occurrence of this event. 7/16
48) If a letter is chosen at random from the English alphabet, find the probability that the letter is
A) a vowel. 5/26
B) a consonant. 23/26
49) In a lottery a person chooses 6 different numbers at random from 1 to 20 and if these 6 numbers match with 6 numbers already fixed by the lottery committee, he wins the price. What is the probability of winning the prize in the game? 21/26
50) Two dice are thrown, find the odds in a favour of getting the sum
A) 4. 1:11
B) 5 1: 8
C) what are the odds against getting the sum 6 ? 31:5
51) What are the odds in favour of getting a spade if the card drawn from a well shuffled deck of cards? What are the odds in a favour of a getting a king. 1:3, 1:12
52) A class consists of 10 boys and 8 girls. Three Students are selected at random. what is the probability that the selected group has:
A) all boys ? 5/34
B) all girls? 7/102
C) one boy two girls? 35/102
D) at least one girl ? 29/34
E) at most one girl ? 10/17
53) A committee of two persons is selected from 2 men and 2 women. what is the probability that the committee will have
A) no man. 1/6
B) one man. 2/3
C) two men.
54) There are four men and six women on the city Councils. if one Council member is selected for a committee at random. how likely is that it is a women. 3/5
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