For a specific location in a particularly rainy city, the time a new thunderstorm begins to produce rain (first drop time) is uniformly distributed throughout the day and independent of this first drop time for the surrounding days. Given that it will rain during some period on both of the next two days, what is the probability that the first drop of rain will be felt between 9:15 AM and 2:50 PM on both days

The required probability = 0.0541

Step-by-step explanation:

From the given information:

The probability that it will rain throughout the day is uniformly distributed & independent of the surrounding days.

Assuming that (P₁)  represents the probability that it will rain between 9:15 am to 2:50 pm on day 1.

The time interval is 5 hours 35 minutes long.

= 5.583333 hours long

Thus;

P₁ = 5.583333/24

P₁ = 0.2326

Assuming that (P₂)  represents the probability that it will rain between 9:15 am to 2:50 pm on day 2.

P₂ = P₁ = 0.2326

Therefore, the total probability = P₂ × P₁  (independent events)

= 0.2326 × 0.2326

= 0.05410276

≅ 0.0541