If there is a 25% chance that it will rain on any given day in Seattle, find the probability that it will rain for three consecutive days.

Question
Probability
asked 2021-01-10
If there is a 25% chance that it will rain on any given day in Seattle, find the probability that it will rain for three consecutive days.

Answers (1)

2021-01-11
Raining on the first day does not affect the probability of raining in the other days so the events are independent.
If A and B are independent events, then:
\(\displaystyle{P}{\left({A}{\quad\text{and}\quad}{B}\right)}={P}{\left({A}\right)}\cdot{P}{\left({B}\right)}\)
Hence,
P(rain and rain and rain)=P(rain)*P(rain)*P(rain)
P(rain and rain and rain)=\(\displaystyle{0.25}\cdot{0.25}\cdot{0.25}\)
P(rain and rain and rain)=\(\displaystyle{0.015625}\to{1.5625}\%\)
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