The US Senate consists of 100 members 2 from each state A co

The U.S. Senate consists of 100 members, 2 from each state. A committee of 8 senators is formed. What is the probability that it contains at least one senator from your state? (Round your answer to two decimal places.)

Solution

Senate members 100

No of senators = 8

No of states = 50

As 2 from each state is selected,

it is certain 2 from your state is selected.

Prob for a random member to be a senator = 0.08

X - no of senators is binomial with p = 0.08

Prob (atleast one senator) is binomial prob for x>=1 with n =2

= 0.1536