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Question
The probability that Mr.Q hits a target at any trial is `1/4`. Suppose he tries at the target 10 times. Find the probability that he hits the target at least one time
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Solution
Let p be the probability of hitting the target
n = 10
p = `1/4`
X = B(n, p)
P(X = x) = ⁿCx px qn-x
x = 0, 1, 2, …. n
q = 1 – p = `3/4`
Probability of hitting at least one time
P(X ≥ 1) = 1 – P(X < 1) = 1 – P(X = 0)
= `1 - ""^10"C"_0 xx (1/4)^0 xx (3/4)^10`
= `1 - 3^10/4^10`
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