In a certain game of chance, your chances of winning are 0.2. if you play the game five times and outcomes are independent, the probability that you win at most once is

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Alexandria Conley

Mathematics

8 March, 08:16

In a certain game of chance, your chances of winning are 0.2. if you play the game five times and outcomes are independent, the probability that you win at most once is

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Bridge · Answer 1

Winning Probablity = 0.2, hence Losing Probability = 0.8 Probablity of winning atmost one time, that means win one and lose four times or lose all the times. So p (W1 or W0) = p (W1) + p (W0) Winning once W1 is equal to L4, winning zero times is losing 5 times. p (W1) = p (W1&L4) and this happens 5 times; p (W0) = p (L5); p (W1) + p (W0) = p (L4) + p (L5) p (L4) + p (L5) = (5 x 0.2 x 0.8^4) + (0.8^5) = > 0.8^4 + 0.8^5 p (W1 or W0) = 0.4096 + 0.32768 = 0.7373