Question

The probability that a mountain bike rider travelling along a certain track will have a tyre bust 0.5 .Find the probability that among 17 riders
i) exactly one has a burst tyre
ii)at most three have a burst tyre
iii) two or more have a burst tyre​

Answer 1

Given :   The probability that a mountain bike rider travelling along a certain track will have a tyre bust 0.5

To find :  i) exactly one has a burst tyre  , ii)at most three have a burst tyre

iii) two or more have a burst tyre​

Solution:

probability of tyre burst p = 0.5

probability of tyre not burst q = 1 - p = 1 - 0.5 = 0.5

number of riders  = 17  

P(x) =  ⁿCₓpˣqⁿ⁻ˣ

i) exactly one has a burst tyre

P(1) = ¹⁷C₁(0.5)¹(0.5)¹⁶   = 17/2¹⁷  =  0.00013

ii)at most three have a burst tyre

= P(0) + P(1) + P(2)   + P(3)

=   ¹⁷C₀(0.5)⁰(0.5)¹⁷ + ¹⁷C₁(0.5)¹(0.5)¹⁶ +  ¹⁷C₂(0.5)²(0.5)¹⁵ + ¹⁷C₃(0.5)³(0.5)¹⁴

= ( 1  + 17 + 136 + 680)/2¹⁷

= 834/2¹⁷

= 0.00636

iii) two or more have a burst tyre​

= 1  - P(0) - P(1)

= 1  -  ¹⁷C₀(0.5)⁰(0.5)¹⁷ - ¹⁷C₁(0.5)¹(0.5)¹⁶

= 1  - (18/2¹⁷)

=  0.99986

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