Assume that the probability of a boy being born is the same as the probability o

Question

Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with four children will have the given composition. (Enter your answer to three decimal places.) Three boys and one girl Assume that the probability of a boy being born Is the same as the probability of a girl being born. Find the probability that a family with three children will have the given composition. (Enter your answer to four decimal places.) At least one girl An exam consists of 15 true-or-false questions. If a student guesses at every answer, what is the probability that he or she will answer exactly 9 questions correctly? Jacobs & Johnson, an accounting firm, employs 16 accountants, of whom 6 are CPAs. If a delegation of 3 accountants is randomly selected from the firm to attend a conference, what is the probability that 3 CPAs will be selected? A shelf in the Metro Department Store contains 95 colored ink cartridges for a popular ink-jet printer. Five of the cartridges are defective. (a) If a customer selects 3 cartridges at random from the shelf, what is the probability that they are all defective? (Round your answer to five decimal places.) (b) If a customer selects 3 cartridges at random from the shelf, what is the probability that at least 1 is defective?

Explanation / Answer

Q-4

P(boy)=P(Girl)=0.5

So, X, the number of boys follows binomial with n=4 and p=0.5

Hence P(3 boys and 1 girsl)=P(X=3)= 0.2500

Q-5

P(boy)=P(Girl)=0.5

So, X, the number of girls follows binomial with n=3 and p=0.5

Hence P(at least 1 girl)=P(X>=1)= 1-P(X=0)=1- 0.1250=0.8750

Q-6

P(true)=P(false)=0.5

So, X, the number of correct follows binomial with n=15 and p=0.5

Hence P(exactly 9 correct)=P(X=9)= 0.153

Q-7

P( 3CPAs)= 6C3/16C3= 0.036

Q-8

Probability of defective =5/95=0.0526

Part-a

Let X be number of defective amongst 3 then X has binomial distribution with n=3 and p=0.0526

So, P(X=3)= 0.00015

Part-b

P(X>=1)=1-P(X=0)=1- 0.850 =0.150

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