Question

1. Chris and Pat both work independently on the same computer program. The probability Chris’ program works is 10% and the probability Pat’s program works is 15%. What is the probability exactly one of their programs works?  

2. Terry and pat both play independently with the same computer game. The probability Terry will score a victory is 30% and the probaabiltythat Pat wwill score a victory is 25%. What is the probability that at least one of them scores a victory?

Answer 1

1) Let P(A) = P(Chris's Program works) = 10% = 0.1

Therefore P(A') = P(Chriss'Program wont work) = 90% = 0.9

Let P(B) = P(Pats Program works) = 15% = 0.15

Therefore P(B') = P(Pats Program wont work) = 85% = 0.85

P(Exactly 1 of the program works) = [P(A) * P(B')] + [P(A') * P(B)]

= (0.1 * 0.85) + (0.9 * 0.15)

= 0.085 + 0.135

= 0.22

Therefore, P(Exactly 1 of the program works) = 0.22 * 100 = 22%

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2) Let P(A) = P(Terry scores a victory) = 30% = 0.3

Therefore P(A') = P(Terry wont score a victory ) = 70% = 0.7

Let P(B) = P(Pat scores a victory) = 25% = 0.25

Therefore P(B') = P(Pat wont score a victory) = 75% = 0.75

P(At least 1 of them scores a victory) = [P(A) * P(B')] + [P(A') * P(B)] + [P(A) * P(B)]

= (0.3 * 0.75) + (0.25 * 0.7) + (0.3 * 0.25)

= 0.225 + 0.175 + 0.075

= 0.475

Therefore, P(At least 1 of them scores a victory) = 0.475 * 100 = 47.5%