Test Index

Probability

Question : 96 of 127

Marks: +1, -0

\frac{1}{3}

the number of girls in the group is

Solution:

Concept:

Use probability formula: number of favorable outcomes divided by total outcomes.

Explanation:

Let number of girls =

n

Total persons =

4 + n

Number of ways to choose 2 girls =

\binom{n}{2} = \frac{n(n-1)}{2}

Number of ways to choose any 2 persons =

\binom{n+4}{2} = \frac{(n+4)(n+3)}{2}

Probability =

\frac{n(n-1)}{(n+4)(n+3)} = \frac{1}{3}

Cross-multiply:

3n(n-1) = (n+4)(n+3)

Expand:

3n^2 - 3n = n^2 + 7n + 12

Simplify:

2n^2 - 10n - 12 = 0

⇒

n^2 - 5n - 6 = 0

Factor:

(n-6)(n+1) = 0

⇒

n = 6

(since

n > 0

Answer:

The number of girls is 6.

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