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If there are g girls and b boys on a team, and two members of the team

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Location: Pakistan
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If there are g girls and b boys on a team, and two members of the team  [#permalink]

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10 Feb 2019, 01:37
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Difficulty:

45% (medium)

Question Stats:

58% (02:14) correct 42% (02:19) wrong based on 12 sessions

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If there are g girls and b boys on a team, and two members of the team are randomly selected, then what is the probability, in terms of g and b, that at least one selected player is a girl?

A. $$\frac{g(g-1)}{(b+g)(b+g-1)}$$

B. $$\frac{b(b-1)}{(b+g)(b+g-1)}$$

C. $$\frac{2bg}{(b+g)(b+g-1)}$$

D. $$\frac{g(2b+g-1)}{(b+g)(b+g-1)}$$

E. $$\frac{b(2g+b-1)}{(b+g)(b+g-1)}$$

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Re: If there are g girls and b boys on a team, and two members of the team  [#permalink]

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10 Feb 2019, 01:57
1
If there are g girls and b boys on a team, and two members of the team are randomly selected, then what is the probability, in terms of g and b, that at least one selected player is a girl?

A. $$\frac{g(g-1)}{(b+g)(b+g-1)}$$

B. $$\frac{b(b-1)}{(b+g)(b+g-1)}$$

C. $$\frac{2bg}{(b+g)(b+g-1)}$$

D. $$\frac{g(2b+g-1)}{(b+g)(b+g-1)}$$

E. $$\frac{b(2g+b-1)}{(b+g)(b+g-1)}$$

Lets donate some values

G = 3, B =2, Total number of ways they can be selected = $$5C_2$$ = 10

Probability(at least 1 girl) = $$3C_1 4C_1+ 3C_2$$ = 9

So are Target value = 9/10

Denominator of all answer options will be 20

Now only D matches our target value

$$\frac{g(2b+g-1)}{(b+g)(b+g-1)}$$

3* (7-1) = 3* 6/20 = 9/10
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Re: If there are g girls and b boys on a team, and two members of the team   [#permalink] 10 Feb 2019, 01:57
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