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# Jan and 5 other children are in a classroom. The principal of the scho

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Math Expert
Joined: 02 Sep 2009
Posts: 56257
Jan and 5 other children are in a classroom. The principal of the scho  [#permalink]

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03 Jan 2019, 04:14
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Difficulty:

15% (low)

Question Stats:

78% (01:13) correct 23% (01:40) wrong based on 50 sessions

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Jan and 5 other children are in a classroom. The principal of the school will choose two of the children at random. What is the probability that Jan will be chosen?

(A) $$\frac{4}{5}$$

(B) $$\frac{1}{3}$$

(C) $$\frac{2}{5}$$

(D) $$\frac{7}{15}$$

(E) $$\frac{1}{2}$$

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Re: Jan and 5 other children are in a classroom. The principal of the scho  [#permalink]

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03 Jan 2019, 04:42
(1C1 * 5C1)/6C2 = 1/3

So option B

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Re: Jan and 5 other children are in a classroom. The principal of the scho  [#permalink]

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03 Jan 2019, 04:45
2

Solution:
Total number of ways of choosing 2 children from 6 children = 6 C 2 = 6!/(4!x2!) = 15 ways
Since the principal of the school will choose two of the children at random and one of them will be Jan, number of ways of another children along with Jan = 5 C 1 = 5 ways
Therefore, probability that Jan will be chosen = 5/15 = 1/3

Alternate Solution:
Given that each children has equal chance of being chosen, when 2 out of 6 children are randomly chosen, then any of 6 children has a chance of 2/6, i.e. 1/3 to be chosen. Therefore, probability that Jan, or any of the other 5 children be chosen is 1/3.

Hence, the Correct Answer is Option B. 1/3

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Re: Jan and 5 other children are in a classroom. The principal of the scho  [#permalink]

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06 Jan 2019, 04:16
Bunuel wrote:
Jan and 5 other children are in a classroom. The principal of the school will choose two of the children at random. What is the probability that Jan will be chosen?

(A) $$\frac{4}{5}$$

(B) $$\frac{1}{3}$$

(C) $$\frac{2}{5}$$

(D) $$\frac{7}{15}$$

(E) $$\frac{1}{2}$$

P of choosing two students out of 6would be 2/6

1/3

IMO B
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Re: Jan and 5 other children are in a classroom. The principal of the scho   [#permalink] 06 Jan 2019, 04:16
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