Election day is less than a month away, and political analysts are focused on the races for two statewide political offices. According to a recent poll, in the race for Governor, 40% of voters support the Republican candidate and 53% of voters support the Democratic candidate. In the race for Attorney General, 61% of voters support the Republican candidate and 37% of voters support the Democrat. Assume that voter preference of candidate for each of the two offices is independent of each other. What is the probability that a randomly selected voter supports both the Democratic candidate for Governor and the Democratic candidate for Attorney General?

Question

Mathematics

Corinne Golden

12 April, 23:22

Election day is less than a month away, and political analysts are focused on the races for two statewide political offices. According to a recent poll, in the race for Governor, 40% of voters support the Republican candidate and 53% of voters support the Democratic candidate. In the race for Attorney General, 61% of voters support the Republican candidate and 37% of voters support the Democrat. Assume that voter preference of candidate for each of the two offices is independent of each other. What is the probability that a randomly selected voter supports both the Democratic candidate for Governor and the Democratic candidate for Attorney General?

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Answers (1)

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Melvin Taylor · Answer 1

0.1961

Step-by-step explanation:

Since these two probabilities are independent of each other, we can simply multiply them.

The probability that a voter will support the Democratic candidate for governor is 0.53.

The probability that a voter will support the Democratic candidate for attorney general is 0.37.

This makes the probability that a voter supports both Democratic candidates 0.53 (0.37) = 0.1961.