Probability that it will rain on the first day and be clear (not rain ) on the next two days is 0.1719 .
<u>Step-by-step explanation:</u>
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.
.
Probability for second day is to not rain i.e.
.
Probability for third day is to not rain i.e.
.
Now, Probability for occurrence of these 3 events simultaneously is :
⇒ ![(0.23)(0.77)(0.77)](https://tex.z-dn.net/?f=%280.23%29%280.77%29%280.77%29)
⇒ ![(0.23)(0.5929)](https://tex.z-dn.net/?f=%280.23%29%280.5929%29)
⇒ ![0.1719](https://tex.z-dn.net/?f=0.1719)
∴ Probability that it will rain on the first day and be clear (not rain ) on the next two days is 0.1719 .