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In a box, there are 40 pens in total in four different colors. There are 12 red pens, 9 blue pens, 10 green pens and 9 black pens. If two pens are chosen at random, what is the chance of getting same color pens?

In a box, there are 40 pens in total in four different colors. There are 12 red pens, 9 blue pens, 10 green pens and 9 black pens. If two pens are chosen at random, what is the chance of getting same color pens? Correct Answer 61/260

GIVEN :

Total number of pens = 40

 

CALCULATION :

Probability of withdrawing 2 pens out of 40 pens = Total outcomes

                                                            = 40C2

                                                            = (40 × 39)/(2 × 1) = 780

Total possible outcomes = (2 pens from 12 red pens) + (2 pens from 9 blue pens) + (2 pens from 10 green pens) + 2 pens from 9 black pens)

⇒ 12C2 + 9C2 + 10C2 + 9C2

⇒ + + +

⇒ 66 + 36 + 45 + 36 = 183

Required Ratio = (Total possible outcome/Total outcomes)

                          = 183/780 = 61/260

∴ Required ratio = 61/260

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