# 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 - Mathematics and Statistics

Sum

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

#### Solution

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

[Note: Answer in the textbook is incorrect.]

Concept: Binomial Distribution
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 8 Binomial Distribution
Miscellaneous exercise 8 | Q 5.1 | Page 254