Question

Quailulduive Aptitude
Question 10 of 20
A box contains 5 green, 3 red and 4 black pens If 2 pens are drawn at random from the box, not replaced and then another pen is drawn What
is the probability of drawing 2 green pens and I black pen?
O 2733
1/14
O2/31
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Answer 1

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Answer 2

The probability of drawing 2 green pens and 1 black pen is $\frac{2}{33}$.

Step-by-step explanation:

Given:

A box contains 5 green, 3 red and 4 black pens.

2 pens are drawn at random from the box, not replaced and then another pen is drawn.

To Find:

The probability of drawing 2 green pens and 1 black pen.

Solution:

As given:A box contains 5 green, 3 red and 4 black pens.

Total nos. of pens= Nos. of green pens+Nos. of red pens+Nos. of black pens.

                             $=5+3+4=12$

Probability of drawing 2 green  pens $=\frac{5C_{2} }{12C_{2} }$

                                                              $=\frac{5 \times2}{11\times6} =\frac{5}{33}$

As given- 2 pens are drawn at random from the box, not replaced and then another pen is drawn.

This means, the pens are not replaced, which reduces the number of pens in the pack to 10.

Therefore, the probability of drawing 1 black pen from a pack of 10 pens $=\frac{4C_{1} }{10C_{1} } =\frac{2}{5}$

Probability of drawing 2 green pens and 1 black pen $=\frac{5}{33} \times\frac{2}{5} =\frac{2}{33}$

Thus,the probability of drawing 2 green pens and 1 black pen is $\frac{2}{33}$.

PROJECT CODE #SPJ2