CIE A level Math -Probability & Statistics 1: 5.4 Discrete random variables: binomial and geometric distributions : Exam Style Questions Paper 5

In a certain country, the probability of more than 10 cm of rain on any particular day is 0.18, independently of the weather on any other day.

Find the probability that in any randomly chosen 7-day period, more than 2 days have more than 10 cm of rain.

Answer/Explanation

Ans:

[P(>2) = 1 – P(0,1,2) =]
1 – (⁷C₀ 0.18⁰ 0.82⁷ + ⁷C₁ 0.18¹ 0.82⁶ + ⁷C₂ 0.18² 0.82⁵)

= 1 – (0.249285 + 0.383048 + 0.252251)
= 1 – 0.88458

0.115

For 3 randomly chosen 7-day periods, find the probability that exactly two of these periods have at least one day with more than 10 cm of rain.

Answer/Explanation

Ans:

[P(at least 1 day of rain) = 1 – P(0) = 1- ( 0.82)⁷ = ] 0.7507

[P(exactly 2 periods) =] 0.7507² × (1 – 0.7507) × 3

0.421