Probability that it will rain on the first day and be clear (not rain ) on the next two days is 0.1719 .
Step-by-step 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. [tex]\frac{23}{100} = 0.23[/tex].
Probability for second day is to not rain i.e. [tex]1-\frac{23}{100} =1- 0.23=0 .77[/tex].
Probability for third day is to not rain i.e. [tex]1-\frac{23}{100} =1- 0.23=0 .77[/tex].
Now, Probability for occurrence of these 3 events simultaneously is :
⇒ [tex](0.23)(0.77)(0.77)[/tex]
⇒ [tex](0.23)(0.5929)[/tex]
⇒ [tex]0.1719[/tex]
∴ Probability that it will rain on the first day and be clear (not rain ) on the next two days is 0.1719 .
