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the probability of winning is half the probability of losing. what is the probability of exactly...

the probability of winning is half the probability of losing. what is the probability of exactly 2 wins in 4 tries?

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Answer #1

The probability of winning is half the probability of losing

Suppose the probability of losing is x, then

Probability of winning = probability of losing / 2 = x/2

But the sum of probability of losing and winning is 1

Therefore, x + (x/2) = 1 = > 3x / 2 = 1 => x = 2/3

Probability of losing = x = 2/3

Probability of winning = x/2 = (2/3)/2 = 2/6

Probability of winning = 2/6

n = 4 trials

P(exactly 2 wins) = P(X = 2)

Here the number of trials and the probability of success is given, so the binomial distribution is applicable

The formula to find the Binomial probability is,

Therefore, the probability that exactly 2 wins in 4 tries is 0.2963

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