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

Question

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}

nikdan · Answer

(1C1 * 5C1)/6C2 = 1/3

So option B

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DisciplinedPrep · Answer

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

Archit3110 · Answer

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

1/3

IMO B

Maria240895chile · Answer

The principal choose 2 times so possibilities of selecting Jan among 6 are:
(First pick is not Jan and second pick is Jan) or (first pick is Jan and second pick is not Jan)

\frac{5}{6}*\frac{1}{5}+\frac{1}{6}*\frac{5}{5} 
 \frac{1}{6}+\frac{1}{6} 
 \frac{2}{6} 
 \frac{1}{3}

*selection without replacement

IMO B

ThatDudeKnows · Answer

No need for nPr or cPr.

There are six spots Jan could fill: Chosen Chosen Not Chosen Not Chosen Not Chosen Not Chosen Each of the six is equally likely. Chosen/Total = 2/6 = 1/3. Answer choice B.

SaquibHGMATWhiz · Answer

Solution:

Number of ways to  choosing Jan   = 1  
 Number of ways of  choosing any one out of 5 other   = 5C1=5

Number of ways of  choosing any two out of 6 children   = 6C2=15

Required probability  =\frac{1*5C1}{6C2}=\frac{1*5}{15}=\frac{1}{3}

Hence the right answer is    Option A

tanvi0915 · Answer

P(JO) where J is Jan and O is other children
= 1/6*5/5*2!(arrangement since jan can be choosen first or second )
= 1/3
 Answer is B

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

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

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