The probability that an event does not happen | vedclass

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(A) Given,probability of failure $q = 0.8$,so probability of success $p = 1 - 0.8 = 0.2$. Number of trials $n = 3$.Using the binomial distribution for

Vedclass · Accepted Answer

$0.896$

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(A) Given,probability of failure $q = 0.8$,so probability of success $p = 1 - 0.8 = 0.2$. Number of trials $n = 3$.Using the binomial distribution formula $P(X = r) = { }^n C_r p^r q^{n-r}$:We need to find the probability that the event happens at most once,which is $P(X \leq 1) = P(X = 0) + P(X = 1)$.$P(X = 0) = { }^3 C_0 (0.2)^0 (0.8)^3 = 1 	imes 1 	imes 0.512 = 0.512$.$P(X = 1) = { }^3 C_1 (0.2)^1 (0.8)^2 = 3 	imes 0.2 	imes 0.64 = 0.384$.Therefore,$P(X \leq 1) = 0.512 + 0.384 = 0.896$.

The probability that an event does not happen in one trial is $0.8$. The probability that the event happens at most once in three trials is:

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