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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 exactly 4 times
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 the target exactly 4 times
P(X = 4) = `""^10"C"_4 xx (1/4)^4 xx (3/4)^6`
= `(10 xx 9 xx 8 xx 7)/(4 xx 3 xx 2) xx 1/4^4 xx 3^6/4^6`
= `210 xx 3^6/4^10`
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