Answer: The probability that no women are chosen to be in the committee is 2/5 or 0.40.
Step-by-step explanation:
We have two positions, and we have 6 options for those positions, 3 are men, and 3 are women.
If we want to see the probability where no women are chosen, then this means that in the first selection a man is chosen.
If all the 6 nominees have the same probability of being chosen, then the probability that in the first selection a man is chosen is equal to the number of men divided the total number of nominees, this is:
p1 = 3/6 = 1/2.
Now the same happens for the second selection, but now we have 5 total nominees and 2 are men, so the probability now is:
p2 = 2/5
And the joint probability will be the product of the individual probabilities, then we have:
P = p1*p2 = (1/2)*(2/5) = 2/5.
The probability that no women are chosen to be in the committee is 2/5 or 0.40.
The probability that no woman is chosen to be on the committee is 0.40.
A club is choosing 2 members to serve on a committee.
The club has nominated 3 women and 3 men.
The number of ways to select two persons from 6 will be:
[tex]\rm = ^6C_2[/tex]
Therefore,
The probability that no woman is chosen to be on the committee is;
[tex]= \dfrac{1}{2} \times \dfrac{2}{5}\\\\= \dfrac{1}{5}\\\\=0.40[/tex]
Hence, the probability that no woman is chosen to be on the committee is 0.40.
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