1) A random variable X.find c
X : 1 2 3 4
P(x): c 2c 3c 4c
A) 0.2 B) 0.3 C) 0.1 D) 0.4
2) A random variable X has:
X: 0 1 2 3
P(x): 2/6 3/6 0/6 1/6 find mean and variance of X are:
A) 1,2 B) 1,3 C) 1,1 D) 3,1
3) Find k from the following:
X: 1 2 3 4
P(x): 2k 4k 3k k
A) 0.2 B) 0.3 C) 0.1 D) 0.5
4) X: -3 -2 -1 0 1 2
P(X): 0.1 2k 3k 7k 0.2 0.1 Find mean
A) 0.25 B) 0.35 C) -0.25 D) -0.35
5) X: 2 4 6 8 10 12
P(X): 0.1 0.2 0.3 0.1 0.1 0.2 Find mean
A) 3 B) 5 C) 7 D) 9
6) A random variable X takes the values 0,1 and 2. if P(X=1)= P(X=2) and P(X=0)=0.4, then the mean of the random variable X is:
A) 1.1 B) 0.9 C) 0.8 D) 0.4
7) A random variable X takes the values 0,1, 2,3 and its mean is 1.3. If P(X=3)= 2P(X=1) and P(X=2)=0.3, then P(X=0)=
A) 0.40 B) 0.30 C) 0.25 D) 0.15
8) A random variable follows Binomial distribution with mean 2 and variance 1.2. then the value of n is:
A) 3 B) 5 C) 7 D) none
9) If in a B. D, np=9 and npq =2.25, then find q
A) 0.75 B) 0.25 C) 0.10 D) 0.45
10) An unbiased dice is tossed 500 times. The standard deviation of the number of 'sixes' in these 500 tosses is:
A) 15/6 B) 51/6 C) 50/6 D) 4/7
11) If in B. D mean= 20, S. D= 4, then p is:
A) 1/5 B) 2/5 C) 3/5 D) 4/5
12) If in B. D mean= 20, S. D= 4, then n is:
A) 119 B) 95 C) 100 D) 105
13) If in B.D , n= 4, p= 1/3, then variance is:
A) 3/8 B) 9/8 C) 8/9 D) 8/3
14) If in B. D mean= 20, S. D= 4, then q is:
A) 5/4 B) 1/5 C) 4/5 D) 2/5
15) 6 coins are tossed. Find the probability of getting
a) all heads.
A) 1/64 B) 15/64 C) 22/64 D) 5/16
b) no heads.
A) 15/64 B) 22/64 C) 5/64 D)1/64
c) Two heads.
A)15/64 B)22/64 C) 5/16 D)31/64
d) Three heads.
A)15/64 B)22/64 C)5/16 D)1/64
e) two or more heads.
A)15/64 B)22/64 C)5/16 D)57/64
f) At most two heads.
A)15/64 B)22/64 C)5/16 D) none
16) Five coin are tossed simultaneously. What is the probability of
a) three heads
A)10/16 B)10/32 C)1/2 D) None
b) at least three heads
A) 1/3 B) 1/32 C) 1/16 D) 1/2
c) more than three heads
A) 5/16 B) 3/16 C) 7/16 D) n
17) A machine produces 2% defectives on an average. If 4 articles are chosen randomly. What is the probability that there will be exactly 2 defective articles?
A)0.229 B)0.115 C)0.235 D)0.452
18) The mean and standard deviation of a binomial distributions are 4 and √(8/3). The values of n and p are:
A) 12, 0.25 B) 12, 0.50
C) 12, 0.75. D) 16, 0.50
19) For a Binomial Distribution the mean is 3 and the variance is 2 .
a) what is the probability of success of the said Binomial Distribution
A)0.50 B) 0.25 C) 0.33 D) 0.65
b) How many times the experiment was repeated?
A) 8 B) 9 C) 10 D) 25
c) what is the probability of failure of the experiment
A)0.50 B) 0.75 C) 0.67 D) 0.5
d) what is the probability that the variable assume the value 5
A)0.2048 B)0.3524 C)0.2456 D) 0.1024
20) For a Binomial distribution, mean is 20 and S. D is 4 .
a) what is the probability of success
A) 0.20 B) 0.30 C) 0.25 D) 0.35
b) what is the value of n
A) 110 B) 90 C) 85 D) 100
c) which of the following gives you the value of q
A) 0.65 B) 0.75 C) 0.80 D) 0.70
21) In a shooting competition, the probability of man hitting a target is 1/5. If he fires 5 times, what is the probability of hitting the target atleast twice?
A) 821/3125 B) 1024/3125
C) 2304/3125 D) none
22) Assume the probability that bomb dropped from an aeroplane will strike a target is 1/5. If 6 bombs are dropped. Find the probability that.
a) Exactly 2 will strike the target
A) 698/3125 B) 768/3125
C) 2304/3125 D) none
b) atleast 2 will strike the target
A) 4536/15625 B) 2596/3125
C) 6533/3125 D) none
22) For a Binomial Distribution, the mean and standard deviation are respectively 5 and 2. Find the probability of getting a non-zero value from the distribution.
A) (0.8)²⁵. B) 1 - (0.8)²⁰
C) 1 - (0.8)²⁵. D) none
23) If the probability of a defective bulb be 1/5. Find the following of a Binomial distribution of defective bulb in a total of 400 bulbs:
a) The mean
A) 8 B) 80 C)10 D) 100
b) the standard deviation:
A) 81 B) 10 C) 16 D) 8
24) The overall percentage of failures in a certain examination is 60. What is the probability that out of a group of 6 candidates atleast 5 passed the examination?
A) (0.4)⁶. B) (0.4)³(0.6)³
C) (0.6)⁵ + (0.6)⁶. D) 4(0.4)⁵
25) 8 coins are tossed 250 times. What is the mean and standard deviation of the distribution thus formed?
A) 8, 2 B) 4, 2 C) 4, 1.41 D) none
26) In 10 independent throws of a defective die, the probability that even number will appear 5 times is twice the probability that the even number will appear 4 times. Find the probability that even number will not appear at all in 10 independent throws of the die.
A) (5/8)¹⁰ B) (3/8)¹⁰
C) (5/8)⁵(3/8)⁵ D) none
27) Suppose that the half the population of a town is a consumers of rice. 100 investigators are appointed to find out its truth. Each investigator interviews 10 individuals. How many investigator do you expect to report that three or less of the people interviewed are consumers of rice.
A) 19 B) 17 C) 21 D) 23
28) The incidence of occupational disease in an individual in such that the workmen have a 20% chance of suffering from it. What is the probability that out of 6 workmen, 4 or more will contact the disease?
A) 353/3125 B) 35/3125
C) 53/3125 D) none
29) Find the probability that in a family of 4 children there will be: (Assuming that the probability of a male birth is 1/2)
a) Atleast 1 boy.
A) 1/16 B) 1- 1/16 C) 1- 1/8 D) 1/8
b) Atleast 1 boy and 1 girl.
A) 1- 1/8 B) 1/8 C) 1/16 B) 1- 1/16
30) Out of 2000 families with 4 children each, how many would you expect to have:
a) Atleast 1 boy
A) 1750 B)1875 C) 750 D) 1000
b) Atleast 1 boy and 1 girl
A) 750 B)1000 C) 1875 D) 1750
c) Exactly 2 girls.
A) 750 B)850 C) 1050 D) 950
31) Four coins are tossed simultaneously, what is the probability of getting two heads and two tails.
A) 2/8 B) 5/8 C) 1- 5/8 D)1- 3/8
32) 6 fair coins are tossed simultaneously. Find the probability of getting:
a) exactly four heads.
A) 13/64 B) 15/64 C) 11/32 D) n
b) at least three heads.
A) 11/32 B) 15/64 C) 1/32 D) n
33) 25% of the inhabitants in a large town are pay bespectacled. what is the probability that a randomly selected group of 6 inhabitants will include at the most 2 bespectacled person.
A) 1701/2408 B) 1809/2048
C) 1701/2048. D) 2048/2480
34) A random variable follows Binomial Distribution with mean 4 and standard deviation √2. find the probability of assuming non zero value of the variant.
A) (0.5) B) (0.5)⁸. C) 1- (0.5)⁸ D) n
35) Assuming the half the population is vegetarian and each of 128 investigators take a sample of 10 individuals to see whether they are vegetarian. How many investigators would you expect to report that two people or less vegetarians.
A) 5 B) 7 C) 9 D) 11
36) The rainfalls on an average 12 days in a month after 30 days. find the probability that a given week:
a) the first four days are fine, remaining wet
A) (0.6)⁴ (0.4)³. B) 35.(0.6)⁴ (0.4)³
C) 35(0.6)³ (0.4)⁴. D) (0.6)³ (0.4)⁴
b) three days are raining.
A) (0.6)⁴ (0.4)³. B) 35.(0.6)⁴ (0.4)³
C) 35(0.6)³ (0.4)⁴. D) (0.6)³ (0.4)⁴
37) A man takes step forward with a probability 0.6 and a step backward with a probability of 0.4. Find the probability that at the end of 11 steps, the man is:
a) one step ahead of starting point
A) (0.6)⁶ (0.4)⁵. B)462.(0.6)⁶ (0.4)⁵
C) 462(0.6)⁵ (0.4)⁶. D) 462(6/25)⁵
b) One step behind of starting point.
A) (0.6)⁶ (0.4)⁵. B) 462(0.6)⁶ (0.4)⁵
C) 462(0.6)⁵ (0.4)⁶. D) 462 (6/25)⁵
c) one step away of starting point
A) (0.6)⁶(0.4)⁵. B)462.(0.6)⁶ (0.4)⁵
C) 462(0.6)⁵ (0.4)⁶. D)462 (6/25)⁵
38) 8 coins are thrown simultaneously. the probability of getting at least 6 heads is:
A) 37/256 B) 73/256
C) 108/256. D) 64/256
39) what is the probability of guessing correctly at least six of the 10 answer in a true - false objective test
A) 139/512. B) 193/512
C) 391/624 D) none
40) A Binomial random variable X satisfies the relation 9P(x= 4)= P(x=2) when n= 6. find the value of the parameter P
A) 1/2 B)!1/3 C) 1/4 D) N
41) in a Binomial Distribution consisting of 5 independent trials, probability of 1 and 2 successes are 0.4096 and 0.2048 respectively. find the parameter P of the distribution ?
A) 1/3 B) 1/4 C) 2/5. D) 1/5
42) The incidence of occupational disease is such that on the average 25% of workers suffer from it. if 10 workers are selected at random, find the probability that:
a) Exactly two workers suffers from the disease.
A) 295245/1048576
B) 551124/1048576
C) 421155/1048576. D) none
b) not more than two workers suffer from the disease.
A) 295245/1048576
B) 551124/1048576
C) 421155/1048576. D) none
43) The overall percentage of failures in a certain examination is 40. what is the probability that out of a group of 6 candidates at least 4 passed the examination?
A) 353/3125. B) 1071/3125
C) 1701/3125. D) none
44) If the probability of defective bolts be 1/10, find the following for the binomial distribution of defective bolts in a total of 400.
a) the mean
A) 20 B) 30 C) 45 D) 40
b) the standard deviation
A) 3 B) 4 C) 5 D) 6
45) Five unbiased coins are tossed simultaneously at random. find the probability of getting
a) Exactly 2 tails
A) 5/16 B) 8/16 C) 13//16 D)14/16
b) at most two tails
A) 14/16 B)13/16 C) 8/16 D)7/16
c) at least 2 tails.
A) 8/16 B) 9/16 C) 12/16 D) 13/16
46) In a binomial distribution with six independent trials, the probability of 3 and 4 successes are found to be 0.245 7 and 0.0819 respectively. Find parameter P of the binomial.
A) 3/13. B) 4/13 C) 5/13 D) 6/13
47) a lot of electronic components is known to contain 20% defective item. 2 person A and H select 8 and 7 components from it. If the total number of defective components found by them is more than two, they reject the lot. Find the probability the lot will be accepted
A) 181/25 (4/5)¹¹. B) (4/5)¹³.
C) 181/25 (4/5)¹³. D) none
48) an experiment succeed twice as often as fails. what is the probability that the next five trials, there will be :
a) 3 successes
A) 77/243 B) 81/243
C) 80/243. D) none
b) at least three successes
A) 80/243 B) 192/243
C) 77/243. D) none
49) An experiments succeeds twice as many times as it fails. find the chance that in 6 trials, there will be at least 5 successes.
A) 256/729 B) 625/729
C) 519/729 D) none
50) an unbiased cubic dice tossed 4 times. what is the probability of obtaining:
a) No six
A) 630/1296. B) 650/1296
C) 526/1296 D) none
b) at least 6
A) 67/1296. B) 76/1296
C) 625/1296 D) 645/1296
c) all odd numbers.
A) 1/4 B) 1/12 C) 15/16 D) 1/16
d) at least one even number
A) 1/4 B) 1/12 C) 15/16 D) 1/16
51) if a dice is thrown 6 times, calculate the probability that:
a) a score of 3 or less occurs on exactly two throws.
A) 15/64 B) 32/66 C)16/64 d) n
b) A score of more than two occurs on exactly 3 throws.
A) 16/729 B)160/729 C)13/729 D)n
c) A score of 5 or less occurs at least once.
A) 46655/46666 B)46655//46656
C) 1/2. D) None
53) The probability that a college student will graduate is 0.4. determine the probability that out of 5 students.
a) one graduate
A) 0.08 B) 0.26 C) 0.92 D) 0.29
b) at least one will be graduate
A) 0.26 B) 0.08 C) 0.299 D) 0.92
54) A coin is tossed 400 times and it shows heads 220 times. Discuss whether the coin is unbiased or not.
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