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Question
6. A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
Solution :
Let X denote the number of balls marked with the digit 0 among the 4 balls drawn.
Since the balls are drawn with replacement, the trials are Bernoulli trials.
X has a binomial distribution with
n
= 4 and p = 1/10
Question
7. In an examination, 20 questions of true-false are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’, if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.
Solution :
Let X represent the number of correctly answered questions out of 20 questions.
The repeated tosses of a coin are Bernoulli trails. Since “head” on a coin represents the true answer and “tail” represents the false answer, the correctly answered questions are Bernoulli trials.
Question
8. Suppose X has a binomial distribution B(6,1/2) Show that X = 3 is the most likely outcome.
Therefore, P (X = 3) is maximum.
Question
9. On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
Solution :
The repeated guessing of correct answers from multiple choice questions are Bernoulli trials. Let X represent the number of correct answers by guessing in the set of 5 multiple choice questions.
Probability of getting a correct answer is,
p
= 1/3
Question
10. A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100 What is the probability that he will win a prize:
(a) at least once
(b) exactly once
(c) at least twice?
Solution :
Let X represent the number of winning prizes in 50 lotteries. The trials are Bernoulli trials.
Clearly, X has a binomial distribution with
n
= 50 and p = 1/100
Question
11. Find the probability of getting 5 exactly twice in 7 throws of a die.
Solution :
The repeated tossing of a die are Bernoulli trials. Let X represent the number of times of getting 5 in 7 throws of the die.
Probability of getting 5 in a single throw of the die,
p
= 1/6
Question
12. Find the probability of throwing at most 2 sixes in 6 throws of a single die.
Solution :
The repeated tossing of the die are Bernoulli trials. Let X represent the number of times of getting sixes in 6 throws of the die.
Probability of getting six in a single throw of die,
p
= 1/6
Let A represents the favourable event i.e., 6
Question
13. It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?
Solution :
The repeated selections of articles in a random sample space are Bernoulli trails. Let X denote the number of times of selecting defective articles in a random sample space of 12 articles.
Clearly, X has a binomial distribution with
n
= 12 and
p
= 10% = 10/100 = 1/10
(D) None of these
Solution :
The repeated selection of students who are swimmers are Bernoulli trials. Let X denote the number of students, out of 5 students, who are swimmers.
Probability of students who are not swimmers,
q
= 1/5
Therefore, option (A) is correct.
