Question

Given that there is a 23% chance it will rain on any day, what is the probability that it will rain on the first day and be clear (not rain ) on the next two days?

Answer 1

Probability that it will rain on the first day and be clear (not rain ) on the next two days is 0.1719 .

Explanation:

We are given that there is a 23% chance it will rain on any day, we need to find what is the probability that it will rain on the first day and be clear (not rain ) on the next two days . Let's do it step by step:

Probability for first day is to rain i.e.
`(23)/(100) = 0.23`.

Probability for second day is to not rain i.e.
`1-(23)/(100) =1- 0.23=0 .77`.

Probability for third day is to not rain i.e.
`1-(23)/(100) =1- 0.23=0 .77`.

Now, Probability for occurrence of these 3 events simultaneously is :

⇒
`(0.23)(0.77)(0.77)`

⇒
`(0.23)(0.5929)`

⇒
`0.1719`

∴ Probability that it will rain on the first day and be clear (not rain ) on the next two days is 0.1719 .