Suppose rain is falling at an average rate of 30 drops per square inch per minute. What is the chance that a particular square inch is not hit by any drops during a given 10-second period? What assumptions are you making?

Using the Poisson distribution, and considering that intervals are independent, it is found that there is a 0.0067 = 0.67% probability that a particular square inch is not hit by any drops during a given 10-second period.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

The parameters are:

In this problem, the rate is of 30 drops per minute, hence, for 10 seconds, considering intervals are independent, the mean is:

The probability that a particular square inch is not hit by any drops during a given 10-second period is P(X = 0), hence:

0.0067 = 0.67% probability that a particular square inch is not hit by any drops during a given 10-second period.

A similar problem is given at link

Therefore the chance that a particular square inch is not by any drops during a given 10 second period is .

Step-by-step explanation:

Poisson distribution:

Given that rain is falling at an average rate 30 drops per square inches per minutes.

A reasonable choose of this distribution is Poisson distribution .

Let the area be a square inch.

Here   = average rate of rain drop × area

           =(30×a)= 30 a      

t = 10 second  .

Therefore,

Therefore the chance that a particular square inch is not by any drops during a given 10 second period is .

the infinity sign

step-by-step explanation:

probability for j is 1/4

while

a is 1/6