Question

In: Statistics and Probability

Jennifer is a competitive runner. In the past she has won 40% of races in within...

Jennifer is a competitive runner. In the past she has won 40% of races in within a season. This season she will compete in 10 races

1. Find the probability that she will will exactly 3 races this season.

2. Find the probability that she will win between 3 and 5 races (inclusive) this season

Expert Solution

Probability of win for Jennifer, w = 0.4

Probability of losing for Jennifer, l = 1 - 0.4 = 0.6.

Jennifer is participating in 10 races.

Probability of winning in n races, P(n) = * wⁿ * l^(10-n) = * 0.4ⁿ * 0.6^(10-n)

1. Probability that she will will exactly 3 races,

P(3) = * 0.4³ * 0.6^(10-3)

P(3) = * 0.4³ * 0.6⁷ = 0.215

2. Probability that she will win between 3 and 5 races (inclusive) :

P(3 X 5) = P(3) + P(4) + P(5) = * 0.4³ * 0.6^(10-3) + * 0.4⁴ * 0.6^(10-4) + * 0.4⁵ * 0.6^(10-5)

P(3 X 5) = 0.2150+ 0.2508 + 0.2007 = 0.6665 = 66.65%.

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orchestra answered 2 years ago

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