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Reptile [31]
2 years ago
8

A company is to hire two employees. They have prepared a final list of eight candidates, all of whom are equally qualified. Of t

hese eight candidates, five are women. If the company decides to select two persons randomly from these eight candidates, what is the probability that:
i. Both candidates are women.
ii. The second candidate is a woman.
iii. The first candidate is a woman given that second one is a woman.
Mathematics
1 answer:
Softa [21]2 years ago
7 0

Answer:

i) Probability that both candidates employed are women = 5/14

ii) Probability that the second candidate is a woman = 5/8

iii) Probability that the first candidate is a woman given that second one is a woman = 4/5

Step-by-step explanation:

Let the probability that a man is employed be P(M) = 3/8

Probability that a woman is employed P(W) = 5/8

a) Probability that both candidates employed are women = (5/8) × (4/7) = 5/14

b) Probability that the second candidate is a woman = (probability that first candidate is a man and second candidate is a woman) + (probability that first candidate is a woman & second candidate is a woman)

= (3/8)(5/7) + (5/8)(4/7) = (15/56) + (20/56) = 35/56 = 5/8

c) Probability that the first candidate is a woman given that second one is a woman

Given that the second candidate was a women, means that the first candidate-women was selected among other four women.

Probability = (4/8)/(5/8) = 4/5

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