3 Assume the likelihood that any computer code works perfect

3. Assume the likelihood that any computer code works perfectly fine is 0.75. We randomly selected four computer codes coded by different programmers. a. What is the probability that all four of the codes are successfully performed? b. What is the likelihood that none of the selected codes are successfully performed? c. What is the likelihood that at least one of the selected codes is successfully performed?

Solution

Since the events are independent,

a) Probability that all codes run perfectly

= 0.75 * 0.75 * 0.75 * 0.75

= 81/256

= 0.3164

b)

Probability that none of them work = ( 1- 0.75) *  ( 1- 0.75) *  ( 1- 0.75) *  ( 1- 0.75)

= 0.25 * 0.25 * 0.25 * 0.25

= 1/256

= 0.00390

c) Probability that atleast one of them works correctly

= 1 - P (None of them work)

= 1 - (1/256)

= 255 /256

= 0.99609

Hope this helps. Ask if you have any doubts.