Question

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

Answer 1

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