LUANDATO wrote:A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not?
A. 1/10
B. 1/5
C. 3/10
D. 2/5
E. 1/2
From the 6 people, 3 will be selected.
Thus, P(Tom is selected) = 3/6 = 1/2.
From the 5 remaining people, 3 will NOT be selected.
Thus, P(Mary is not selected) = 3/5.
To combine these probabilities, we multiply:
1/2 * 3/5 = 3/10.
The correct answer is
C.
Alternate approach:
ONE WAY:
One way to yield a favorable outcome is to choose Aaron first.
P(1st person selected is Aaron) = 1/6.
P(2nd person selected is not Karen) = 4/5. (Of the 5 remaining people, anyone but Karen.)
P(3rd person selected is not Karen) = 3/4. (Of the 4 remaining people, anyone but Karen.)
To combine these probabilities, we multiply:
1/6 * 4/5 * 3/4 = 1/10.
OTHER WAYS:
Since a favorable outcome will be achieved if Aaron is chosen 1st, 2nd, or 3rd -- for a total of 3 ways -- we multiply by 3:
1/10 * 3 = 3/10.
The correct answer is
C.
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