Question

Suppose that 5 men out of 100 and 25 women out of 1000 are good orators. Assuming there are equal number of men and women, find the probability of choosing a good orator.

(Baye's Theorem,Probability)

Answer 1

3.75%

Explanation:

The probability of choosing a good orator from the male population is 5/100 or 0.05, and the probability of choosing a good orator from the female population is 25/1000 or 0.025.

Since there are equal numbers of men and women, the probability of choosing a male or a female is 0.5.

To find the probability of choosing a good orator, we can use the law of total probability:

P(good orator) = P(good orator|male) * P(male) + P(good orator|female) * P(female)

Plugging in the values, we get:

P(good orator) = 0.05 * 0.5 + 0.025 * 0.5 = 0.0375

Therefore, the probability of choosing a good orator is 0.0375 or 3.75%.