Question

There are 5 red pens, 3 blue pens and 2 green pens in a box. Ziyad takes at random a pen from the box and gives the pen to his friend, Tamer. Ziyad then randomly takes another pen from the box. Work out the probability that both pens are the same color.

Answer 1

Answer: 14/45

Explanation:

Assuming that there is no replacements:

The probability of both pens being red will be represented by P(r), and P(b) and P(g) will represents both being blue and green respectively

P(r) = 5/10 x 4/9 = 2/9

P(b) = 3/10 x 2/9 = 1/15

P(g) = 2/10 x 1/9 = 1/45

Now take all 3 probabilities and add them all together to find the probability that any 2 pen will be the same color

P = P(r) + P(b) + P(g)

P = 2/9 + 1/15 + 1/14

P = 14/45