Question

A bag contains 5 pink hats and 7 maroon hats. Two hats are drawn at random. What is the probability of both being of the same color?

1. 31 / 66
2. 21 / 66
3. 1 / 6
4. 31 / 60
5. 21 / 60

Answer 1

Correct Answer - Option 1 : 31 / 66

Given:

Pink hats = 5

Maroon hats = 7

Calculation:

Total number of outcomes = ¹²C₂

⇒ ¹²C₂ = 12! / (10! × 2!)

⇒ ¹²C₂ = 6 × 11

⇒ ¹²C₂ = 66

There exist two cases, Both hats either of pink color or of maroon colors

⇒ Possible outcomes = ⁵C₂ + ⁷C₂

⇒ Possible outcomes = (5! / (3! × 2!)) + (7! / (5! × 2!))

⇒ Possible outcomes = 10 + 21

⇒ Possible outcomes = 31

Probability = 31 / 66

∴ Probability of hat being of same color is 31 / 66