X: 1 2 3
F(X): 2p p 4p find
A) E(x). 2.29
B) V(x). 0.78
C) Pr(x> 1). 5/7
2) A random variable x has the following Probability distribution:
x: 0 1 2 3 4 5 6 7 8
P(x): k 2k 4k 6k 8k 10k12k 14k 16k
Find
A) E(x). 5.59
B) V(x). 4.27
C) p(x <3). 7/73
D) p(x ≥ 3). 66/73
E) p(0< x < 5). 20/73
3) If a coin is tossed 3 times, obtain the p.m.f. of the number of heads. Hence obtain its probability distribution.
4) A box contains 4 and 3 white balls. If 2 balls are drawn from this box, find the p.m.f. of the number of red balls and hence obtain its probability distribution.
5) The mean of a Binomial Distribution is 4 and the standard deviation is 3 -- This statement can not be true, why ?
6) For a Binomial Distribution, the mean is 3 and variance is 2. Find the value of n and p. Hence find the probability that X (the variable value) is 5. 9, 1/3, 224/2187
7) If the mean and the variance of a Binomial distribution are respectively 4 and 8/3, find the values of n and p. 12, 1/3
8) The mean of a Binomial Distribution is 40 and standard deviation is 6. Calculate n, p and q. 400, 1/10, 9/10
9) In a Binomial distribution consisting of 5 independent trials, Probabilities of 1 and 2 success are 0.4096 and 0.2048 respectively. Find the parameter p of the distribution. 1/5
10) With usual notations, find p for a Binomial random variable X if n= 6, and if P(X= 4) = P(X= 2). 1/4
11) An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be
A) three success. 80/243
B) at least three success. 64/81
12) An experiment succeed twice as many as times as it fails. Find the chance that in 6 trials, there will be at least five success. 256/729
13) Four coins are tossed simultaneously. What is the probability of getting 2 heads and 2 tails. 31/81
14) Eight coins are thrown simultaneously. Find the chance of obtaining.
A) atleast 6 heads. 37/256
B) no heads. 1/256
C) all heads. 1/256
15) If ten fair coins are tossed, what is the probability that are n of getting to tell you fire point are not more than three heads. 11/64
16) A dice thrown three times. If getting a six is considered a success, find the probability of getting atleast two success. 2/27
17) If 10 coins are tossed 100 times. How many times would you except 7 coins to fall head upward ? 12
18) What is the probability that if a fair coin is tossed 6 times we will get:
A) exactly two heads ? 15/64
B) at least 2 heads. 57/64
19) An unbiased cubic die is tossed 4 times. What is the probability of getting
A) no six. 625/1296
B) least one six. 671/1296
C) all odd numbers. 1/16
D) atleast one even number. 15/16
20) If a die is thrown six times, calculate the probability that:
A) a score of 3 or less occurs on exactly 2 throws. 15/64
B) a score of more than 2 occurs on exactly 3 throws. 160/729
C) a score of 5 or less occurs atleast once. 46655/46656
D) a score of two or less occurs on at least five occasions. 13/729
21) Assume that on an average one telephone out of 10 is busy. 6 telephone numbers are randomly selected and called. Find the probability that four of them will be busy. 0.001215
22) The probability that a college student will be graduate is 0.4. Determine the probability that out of 5 students
A) none. 0.08
B) one. 0.26
C) atleast one will be graduate. 0.92
23) A machine produces 2% of defectives on the average. If 4 articles, are chosen randomly, what is the probability that there will be exactly 2 defective articles. 0.0023
24) 25% of the inhabitants in a large town are bespectacled. What is the probability that a randomly selected group of 6 inhabitants will included Atmost 2 bespectacled persons. 1701/2048
25) The overall percentage of failures in a certain examination is 40. What is the probability that out of a group of 6 candidates atleast 4 passed the examination ? 1701/3125
26) Find the probability that in a family of 5 children there will be
A) at least one boy.
B) at least one boy and one girl. (Assume that the probability of a female birth is 1/2). 31/32, 15/16
27) In a shooting competition, the probability of a man hitting a target is 1/5. If he fires 5 times, What is the probability of hitting the target atleast twice ? 821/3125
28) The incidence of occupational disease in an industry is such that the workers have a 20% chance of suffering from it. What is the probability that out of 6 workers, 4 or more will contact the disease ? 53/3125
29) In 10 independent throws of a defective die, the probability that an even number will appear 5 times is twice the probability that an even number will appear 4 times. Find the probability that an even number will not appear at all in 10 independent throws of the die. (3/8)¹⁰
30) Suppose that half the population of a town are consumers of rice. 100 investigators are appointed to find out its truth. Each investigator interview 10 individual. How many investigators do you expect to report that three or less of the people interviewed are consumers of rice. 17
31) If on the average rainfalls on 12 days in every 30 days, find the probability
A) that the first four days of a given week will be fine, and the remainder wer. 648/78125
B) that rain will fail on just 3 days of a given week. 4536/15625
32) A coin is tossed 8 times. Find the probability of getting
A) three times head. 7/32
B) first three times head. 1/256
33) A die is tossed 5 times. Find the probability of getting face 6.
A) 3 times. 125/3888
B) at least three times. 23/648
C) atmost three times. 3875/3888
D) first three times. 25/7776
34) A machine produces 25% defective items. From a day's production two samples of size 7 and 5 are chosen at random. Find the probability that two samples together will contain more than 25% defective items. 0.35
35) Three fair coins are tossed 3000 times. Find the frequency distribution of number of heads, calculate mean and standard deviations of the distribution. 1500, 27.38
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