9) Suppose E and F are events in a sample space and p(E)-3/4, p(F) = 4/5, and p(

Question

9) Suppose E and F are events in a sample space and p(E)-3/4, p(F) = 4/5, and p(F | E)-78. Find p(E | F). 10) This question deals with buying and using a pair of thumb drives. (a) The probability a thumb drive you buy is defective is.002. Assume that the probability one thumb drive is defective does not affect the probability of another one being defective. Given that you've bought two thumb drives, what is the probability that both are defective? (b) Luckily, both of the thumb drives you've bought work! Each has 1 GB of memory available for you to save files. You have four files you would like to save on the two thumb drives of the following sizes: .7 GB, 4 GB, .3 GB and .3 GB. Unfortunately, you've left your nimwit brother to copy the files from your desktop to the two thumb drives. For each of the four files, he randomly chooses one of the two thumb drives to copy the file, not checking if the copy was successful. (Assume a copy successful as long as the requisite space is available.) What is the probability that all four files get copied successfully? Leave your answer as a fraction in lowest terms.

Explanation / Answer

9)

Solution :

Given that ,

p(E) = 3 / 4

p(F) = 4 / 5

p(F | E) = 7 / 8

so , p(E | F) = (p(F | E) * p(E) )/ p(F)

= ((7 / 8) * (4/5)) / 3 / 4

= 112 / 120

p(E | F) = 14 / 15 = 0.93

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