The probability that an event A happens in a | vedclass

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Question

(A) Let $p$ be the probability of event $A$ happening in a single trial,so $p = 0.4$. Let $q$ be the probability of event $A$ not happening in a singl

Vedclass · Accepted Answer

$0.784$

Vedclass · Answer

(A) Let $p$ be the probability of event $A$ happening in a single trial,so $p = 0.4$. Let $q$ be the probability of event $A$ not happening in a single trial,so $q = 1 - p = 1 - 0.4 = 0.6$. We are performing $n = 3$ independent trials. The probability that event $A$ happens at least once is given by $P(X \geq 1) = 1 - P(X = 0)$. Using the binomial distribution formula,$P(X = 0) = ^nC_0 	imes p^0 	imes q^n$. Substituting the values,$P(X = 0) = 1 	imes (0.4)^0 	imes (0.6)^3 = 1 	imes 1 	imes 0.216 = 0.216$. Therefore,$P(X \geq 1) = 1 - 0.216 = 0.784$.

The probability that an event $A$ happens in a trial is $0.4$. If three independent trials are made,then the probability that $A$ happens at least once is

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