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.
Mathematics · High School · Tue Nov 03 2020
Answered on
Given :
Number of red pens = 5
Number of blue pens = 3
Number of green pens = 2
Total possibilities = 12C2
Formula:
nCr = n!/r!(n-r)!
12C2 = 12!/2!(12-2)!
= 12 × 11 × 10!/2 × 10!
= 6 × 11
= 66
Now, for two pens of same color :
5C2 + 3C2 + 2C2
= 5!/2! × 3! + 3!/2! × 1! + 2!/2! × 1!
= 5 × 4 × 3!/2 × 3! + 3 × 2!/2! + 1
= 10 + 3 + 1
= 14
Now, probability of selecting two pens of same color = 14/66
= 7/33