Answer to Question #242970 in Statistics and Probability for Viraj Rambhia

Question

Calculate the probabilities for the following statements as per the given scenario. A study undertaken by the Rajan Supervisor of Elections in 2002 revealed that 44% of registered voters are ‘Dharwadi Yuth’, 37% are Rajmoti, and 19% are others. If two registered voters are selected at random, what is the probability that both of them have the same party affiliation?

Answer 1

Given that:

Calculate the probabilities for the following statements as per the given scenario and draw the probability tree diagram also.

A study undertaken by the Rajan Supervisor of Elections in 2002 revealed that 44% of registered voters are ‘Dharwadi Yuth’, 37% are Rajmoti, and 19% are others. 

Let's denote Dharwadi tuth by D, rajmoti by R, and Others by O.

We are given:

P(D)=0.44, P(R)=0.37, P(O)=0.19

the probability that both of them have the same party affiliation is:

P(Both same af filiation)=P(Both D) +P(Both R) + P(Both O)

=(0.44*0.44) + (0.37*0.37) +(0.19*0.19)

= 0.1936+0.369+0.0361

=0.3666

The tree diagram for the given statement is: