Radioactive mass A emits particles at a mean rate of 20 per minute, and radioactive mass B emits particles at a mean rate of 25 per minute.

a. What is the probability that fewer than 200 particles are emitted by both masses together in a five- minute time period?

b. What is the probability that mass B emits more particles than mass A in a two-minute time period?

Solution

Step 1 of 4

Let X represents the no. of particles emitted by radioactive mass A

Let Y represents the no. of particles emitted by radioactive mass B

a) Here we have to find the probability that fewer than 200 particles are emitted by both A and B together in 5 minutes time period

In 1 minutes time period no. of particles emitted by A is 20

In 5 minutes time period no. of particles emitted by A is 20(5)=100

In 1 minutes time period no. of particles emitted by B is 25

In 5 minutes time period no. of particles emitted by B is 25(5)=125

Here X and Y follows the poisson distribution

XPoisson(100)

YPoisson(125)

Here X follows the normal distribution with mean 100 and standard deviation 100

Here Y follows the normal distribution with mean 125 and standard deviation 125