Bunuel wrote:
A coed soccer team has W women and M men on the team. If 4 women and 2 men are added to the team roster, and if one person on the team is selected at random to serve as team captain, then the probability that the team captain will be a woman can be represented as
A. (W + 4)/(W + M + 6)
B. (W + 4)/(W + M + 2)
C. (W + 4)/(M + 2)
D. (W + 4)/(W + M)
E. W/M
These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
The two posters above have solved the question algebraically, so let's use the INPUT-OUTPUT approach.
Let's choose values for W and M and then answer the question.
Let W = 1 and let M = 1
So, to start, the team consists of 1 woman and 1 man.
4 women and 2 men are added to the team roster...Now the number of women on the team = 1 + 4 = 5
And the number of men on the team = 1 + 2 = 3
So, there are 8 people on the team
...if one person on the team is selected at random to serve as team captain, then the probability that the team captain will be a woman can be represented asThere are now 8 people on the team and 5 are women.
So, P(a woman is selected) = 5/8
So, when we INPUT W =
1 and M =
1, the answer to our question (i.e., the OUTPUT) is
5/8Now, we'll check each answer choice, and see which one yields an OUTPUT of
5/8 when we replace W with
1 and M with
1A. (
1 + 4)/(
1 +
1 + 6) =
5/8 - PERFECT - KEEP A
B. (
1 + 4)/(
1 +
1 + 2) =
5/4 - No good. ELIMINATE B
C. (
1 + 4)/(
1 + 2) =
5/3 - No good. ELIMINATE C
D. (
1 + 4)/(
1 +
1) =
5/2 - No good. ELIMINATE D
E.
1/
1 =
1 - No good. ELIMINATE E
Answer: A
Cheers,
Brent
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