Chapter 13 Probability Ex 13.5 Solutions
Question - 11 : - Find the probability of getting 5 exactly twice in 7 throws of a die.
Answer - 11 : -
Let us assume Xrepresent the number of times of getting 5 in 7 throws of the die
Also, the repeatedtossing of a die are the Bernoulli trials
Thus, probability ofgetting 5 in a single throw, p = 1/6
And, q = 1 – p
= 1 – 1/6
= 5/6
Clearly, we have X hasthe binomial distribution where n = 7 and p = 1/6
Question - 12 : - Find the probability of throwing at most 2 sixes in 6 throws of a single die.
Answer - 12 : -
Let us assume Xrepresent the number of times of getting sixes in 6 throws of a die
Also, the repeatedtossing of die selection are the Bernoulli trials
Thus, probability ofgetting six in a single throw of die, p = 1/6
Clearly, we have X hasthe binomial distribution where n = 6 and p = 1/6
And, q = 1 – p =1 – 1/6 = 5/6
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?
Answer - 13 : -
Let us assume Xrepresent the number of times selecting defected articles in a random samplespace of given 12 articles
Also, the repeatedarticles in a random sample space are the Bernoulli trials
Clearly, we have X hasthe binomial distribution where n = 12 and p = 10% = 1/10
And, q = 1 – p = 1 –1/10 = 9/10
Question - 14 : - In a box containing 100 bulbs, 10 are defective. The probability that outof a sample of 5 bulbs, none is defective is
A. 10–1
B. (1/2)5
C. (9/10)5
D. 9/10
Answer - 14 : -
C. (9/10)5
Explanation:
Let us assume Xrepresent the number of times selecting defected bulbs in a random sample ofgiven 5 bulbs
Also, the repeatedselection of defective bulbs from a box are the Bernoulli trials
Clearly, we have X hasthe binomial distribution where n = 5 and p = 1/10
And, q = 1 – p = 1 –1/10
Question - 15 : - The probability that a student is not a swimmer is 1/5. Then theprobability that out of five students, four are swimmers is
A. 5C4 1/5 (4/5)4
B. (4/5)4 (1/5)
C. 5C1 1/5 (4/5)4
D. None of these
Answer - 15 : -
A. 5C4 1/5(4/5)4
Explanation:
Let us assume Xrepresent the number of students out of 5 who are swimmers
Also, the repeatedselection of students who are swimmers are the Bernoulli trials
Thus, probability ofstudents who are not swimmers = q = 1/5
Clearly, we have X hasthe binomial distribution where n = 5
And, p = 1 – q
= 1 – 1/5
= 4/5
