A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______.
Correct Answer
Solution & Step-by-step Explanation
In the range: 0.65 - 0.65
Concept:
M for men, W for women, E for employed & U for unemployed
Referring to the diagram below,
∴ Total probability when the selected person is unemployed,
P(U) = P(M). P(U/M) + P(W) ⋅ P(U/W) ...(1)
Total probability when the selected person is emlpoyed,
⇒ P(E) = 1 – P(U) ...(2)
Calculation:
Given:
P(M) = 0.5, P(W) = 0.5, P(U/M) = 0.2 & P(U/W) = 0.5
Using equation (1),
⇒ P(U) = (0.5× 0.2) + (0.5× 0.5)
⇒ P(U) = 0.35
Using equation (1),
⇒ P(E) = 1 - 0.35
⇒ P(E) = 0.65
Concept:
M for men, W for women, E for employed & U for unemployed
Referring to the diagram below,
∴ Total probability when the selected person is unemployed,
P(U) = P(M). P(U/M) + P(W) ⋅ P(U/W) ...(1)
Total probability when the selected person is emlpoyed,
⇒ P(E) = 1 – P(U) ...(2)
Calculation:
Given:
P(M) = 0.5, P(W) = 0.5, P(U/M) = 0.2 & P(U/W) = 0.5
Using equation (1),
⇒ P(U) = (0.5× 0.2) + (0.5× 0.5)
⇒ P(U) = 0.35
Using equation (1),
⇒ P(E) = 1 - 0.35
⇒ P(E) = 0.65