Question

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 at some point both of the next two days, what is the probability that the first drop of rain will be felt between 8: 40 AM and 2: 35 PM on both days? a) 0.2479 Web) 0.0608 om c) 0.2465 d) 0.9385 e) 0.0615 f) None of the above.

Answer 1

b) 0.0608

Explanation:

As it is mentioned that the next two days i.e 24 hours, the probability of the rain is uniformly distributed

Therefore the rain probability is

`= (T)/(24)`

where,

T = Length of the time interval

Plus, as we know that rain is independent

So let us assume the rain between the 8: 40 AM and 2: 35 PM on single day is P1 and the time interval is 5 hours 55 minutes

i.e

= 5.91666 hours long.

So, P1 should be

`= (5.91666)/(24)`

= 0.2465

Now we assume the probability of rain on day 2 is P2

So it would be same i.e 0.2465

Since these events are independent

So, the total probability is

`= 0.2465 * 0.2465`

= 0.0608

Hence, the b option is correct