Question

A radio active source emits on the average 2.5 particles per second. Calculate the probability that 3 0r more particles will be emitted in an interval of 4 seconds.Assume the radio active emission follows Poisson distribution.
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Answer 1

Given : A radio active source emits on the average 2.5 particles per second.

To Find : Calculate the probability that 3 0r more particles will be emitted in an interval of 4 seconds.

Solution:

P(x)  = λˣ  e^(-λ) / x!

average emit per second = 2.5

average emit per 4 seconds = 2.5 x 4 = 10

3 or more particles will be emitted in an interval of 4 seconds  

= 1  - P(0) - P(1) - P(2)

λ = 10

P(0)  =  10⁰  e⁻¹⁰/ 0!    =   4.54 x 10⁻⁵ = 0.0000454

P(1)  =  10¹  e⁻¹⁰/ 1!    =     4.54 x 10⁻⁴ = 0.000454

P(2)  =  10² e⁻¹⁰/ 2!    =    0.00227

0.0000454 + 0.000454 + 0.00227

= 0.0027694

1  - 0.0027694  = 0.9972306

= 0.997

Probability that 3 0r more particles will be emitted in an interval of 4 seconds.  = 0.997

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