Respuesta :
Answer:
(a) The probability that a worker who is unemployed is a man is 0.5384.
(b) The probability that a worker who is unemployed is a woman is 0.3953.
Explanation:
Let's denote the events as follows:
U = An eligible person is unemployed
M = An eligible person is a man
W = An eligible person is a woman
Given:
P (U) = 0.085, O (U | M) = 0.088, P (U | W) = 0.070 and P (M) = 0.52.
The probability that an eligible person is a woman is,
P (W) = 1 - P (M) = 1 - 0.52 = 0.48
(a)
It is provided that a worker is unemployed.
Determine the probability that the worker is a man as follows:
[tex]P(M|U)=\frac{P(U|M)P(M)}{P(U)}= \frac{0.088\times0.52}{0.085}= 0.5384[/tex]
Thus, the probability that a worker who is unemployed is a man is 0.5384.
(b)
It is provided that a worker is unemployed.
Determine the probability that the worker is a woman as follows:
[tex]P(W|U)=\frac{P(U|W)P(W)}{P(U)}= \frac{0.07\times0.48}{0.085}= 0.3953[/tex]
Thus, the probability that a worker who is unemployed is a woman is 0.3953.
