Hi, I could use help step by step for this problem I am really struggling with p

Question

Hi, I could use help step by step for this problem I am really struggling with probability and hope that following along will make it more clear! thank you in advance!

3.27 A technician is assigned the task of examining transistors before they are installed into a radio. She has a box containing 12 transistors, 3 of which are defective. (a) Suppose 2 transistors are randomly selected with replacement. Find the proba- bility that both are defective (i.e. find P(Di and D2)). Assume independence. Statistics for Business, University of loud, ©2017 Matt Bognar .6 ExERCISES 49 (b) Suppose 2 transistors are randomly selected with replacement. Find the proba- bility that the first is defective or the second is defective, i.e. find P(D1 or D2) (c) Suppose 2 transistors are randomly selected without replacement. Given that the first transistor is defective, determine the probability that the second transistor is defective (i.e. find P(2 (d) Suppose 2 transistors are randomly selected without replacement. Find the prob- ability that both are defective (i.e. find P(Di and D2)) e) Suppose 2 transistors are randomly selected without replacement. Find the prob- ability that the first is defective or the second is defective, i.e. find P(Di or D2) Hint: Use the law of total probability to find P(D2)

Explanation / Answer

a) probability that both are defective P(D1 and D2)=(3/12)*(3/12) =0.0625

b)P(D1 or D2 )= 1-P( both are not defective) =1-(1-3/12)*(1-3/12) =0.4375

c)for without replacement:

P(D1) =3/12

and P(D1 and D2) =(3/12)*(2/11)

therefore P(D2|D1) =P(D1 and D2)/P(D1) ==(3/12)*(2/11) /(3/12) =2/11

d) from above P(D1 and D2) = =(3/12)*(2/11) =1/22

e)P(D1 or D2 )=1-P( both are not defective) =1-(9/12)*(8/11) =0.4545

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