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: - $A$ be the event that a randomly chosen person is a woman. - $B$ be the event that a randomly chosen person works outside the village. We are given: - $P(A) = \frac{4000}{8000} = 0.5$ (probability of being a woman), - $P(B) = \frac{3000}{8000} = 0.375$ (probability of working outside the village), - $P(A \cap B) = 0.3 \times 0.5 = 0.15$ (probability of being a woman and working outside the village). We want to find $P(A \cup B)$, the probability of either being a woman or working outside the village: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.5 + 0.375 - 0.15 = 0.725 \] Thus, the probability that a randomly chosen individual is either a woman or a person working outside the village is 0.725.