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प्रश्न
The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: exactly one has a burst tyre
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उत्तर
Let X = number of burst tyre.
p = probability that a mountain-bike travelling along a certain track will have a tyre burst
∴ p = 0.05
∴ q = 1 - p = 1 - 0.05 = 0.95
Given: n = 17
∴ X ~ B(17, 0.05)
The p.m.f. of X is given by
P(X = x) = `"^nC_x p^x q^(n - x)`
i.e. p(x) = `"^17C_x (0.05)^x (0.95)^(17 - x)`, x = 0, 1, 2,...,17
P(exactly one has a burst tyre)
P(X = 1) = p(1) = `"^17C_1 (0.05)^1 (0.95)^(17 - 1)`
`= 17(0.05)(0.95)^16`
`= 0.85 (0.95)^16`
Hence, the probability that riders has exactly one burst tyre = (0.85)(0.95)16
Notes
The answer in the textbook is incorrect.
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