Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are

Question

Mr. Yutaro’s class contains 5 boys and 11 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?

A. 9/48
B. 9/20
C. 11/24
D. 27/48
E. 13/16

BrentGMATPrepNow · Accepted Answer

P(1 boy and 1 girl chosen) = P(1st selection is boy   AND   2nd selection is girl   OR   1st selection is girl   AND   2nd selection is boy) 
= P(1st selection is boy   AND   2nd selection is girl)   +   P(1st selection is girl   AND   2nd selection is boy) 
= P(1st selection is boy)   x   P(2nd selection is girl)   +   P(1st selection is girl)   x   P(2nd selection is boy) 
= 5/16   x   11/15   +   11/16   x   5/15
= 55/240   +   55/240
= 110/240
= 11/24 
= C

Cheers,
Brent

andrewcs · Answer

Probability of a boy being chosen first, then a girl:
5/16 * 11/15

Probability of a girl being chosen first, then a boy:
11/16 * 5/15

Probability of a boy and a girl being chosen:
(5*11+5*11) / (15*16)
=11+11/3*16
=22/48
=11/24, so C.

umeshkathuria · Answer

(5C1*11C1)/16C2 = 11/24

BarneyStinson · Answer

Actually, problems of this kind, prefer subtracting from all possible probabilities = 1.

Subtract probability of choosing only two boys and probability of choosing only two girls and that should give the final answer. This will be more helpful when you have many more selections that happen and not just 2 and one from each is required.

bangalorian2000 · Answer

Ways to choose one boy = 5c1 = 5
Ways to choose one girl = 11c1 = 11

Total ways = 16c2 = 16*15

p=(5*11)/16*15 - 11/24 hence C

luffy_ueki · Answer

Number of ways of selecting two students from the class of 5 boys & 11 girls = 16C2 (total) =15*16/2
Number of ways of selecting 1 boy & 1 girl = 5C1 * 11C1 = 5*11
probability = 5*11/15*8 = 11/24

ScottTargetTestPrep · Answer

The probability that a girl and a boy, in that order, are chosen is 11/16 x 5/15 = 11/16 x 1/3 = 11/48. The probability that a boy and a girl, in that order, are chosen is also 11/48. Therefore, the probability that a boy and a girl are chosen is 11/48 + 11/48 = 22/48 = 11/24.

Answer: C

mvdst99 · Answer

2
 1 x 5/16 x 11/15 = 110/240 = 11/24

2
1 indicates that there's two possibilities to choose one girl and one boy, e.g. 5/16 x 11/15 or 11/16 x 5/15

2
1 is combinatorial, and in this case it will just be (2!)/(1!x1!) = 2

alexisrakh · Answer

(5/16)(11/15)*2! = 11/24
 boy girl

Posted from my mobile device

ramlala · Answer

1. First boy and than Girl

= \frac{5}{16} * \frac{11}{15}

= \frac{11}{48}

2. First Girl and than Boy

= \frac{11}{48}

Total =  \frac{11}{48} + \frac{11}{48}

=  \frac{11}{24}

Ans C

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