Suppose that a population of registered voters contains 10% registered Democrats

Question

Suppose that a population of registered voters contains 10% registered Democrats, and that 90% of registered Democrats typically vote for the Democrat candidate. The Democrat candidate in this election is particularly popular and gathers 50% of voters who are not registered Democrats. A voter exits from the voting booth and announces truthfully that she has voted for the Democrat candidate. What is the probability that she is a registered Democrat?

.75 or greater.

Greater than or equal to .5 but less than .75.

Greater than .25 but less than .5

Less than or equal to .25.

.75 or greater.

Greater than or equal to .5 but less than .75.

Greater than .25 but less than .5

Less than or equal to .25.

Explanation / Answer

Correct option:

Less than or equal to .25

EXPLANATION:

From the given data, the following Table is formed:

                          Registered Democrat             Not Registered                     Total

Voted for Democrat     9                                   45                                    54

Did not vote for Democrat                   1                                   45                                   46

Total                                               10                                   90                                 100

P(Registered Democrat/Voted for Democrat)

= P(Registered Democrat & Voted for Democrat)/ P(Voted for Democrat)

= 9/54 = 0.1667

So, correct option:

Less than or equal to .25

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