Question

(b) In a village of 8000 people, 3000 go out of the village to work and 4000 are women. It is noted that 30% of women go out of the village to work. What is the probability that a randomly chosen individual is either a woman or a person working outside the village?

Hint:

To find the probability of the union of two events, use the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.

Answer 1

Let event $A$ represent a randomly chosen person being a woman and event $B$ represent a randomly chosen person working outside the village. We are given the following probabilities: $P(A) = \frac{4000}{8000} = 0.5$, $P(B) = \frac{3000}{8000} = 0.375$, and $P(A \cap B) = 0.3 \times 0.5 = 0.15$. We aim to calculate $P(A \cup B)$, the probability that a person is either a woman or works outside the village. Using the formula for the union of two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.5 + 0.375 - 0.15 = 0.725 \] Consequently, the probability that a randomly selected individual is a woman or works outside the village is 0.725.