The urn contains 5 red balls and 3 white ones. 2 balls are drawn at random.

The urn contains 5 red balls and 3 white ones. 2 balls are drawn at random. What is the probability that both balls are red?

Let’s count the number of balls – only 8 balls.

The outcome is the choice of any 2 balls.

The number of all outcomes is C2 8 = 8! / (2! * 6!) = 40320/2 * 720 = 40320/1440 = 28.

Favorable outcome – choice of 2 red balls.

2 red balls out of 5 can be chosen in C25 ways.

C25 = 5! / (2! * 3!) = 120/2 * 6 = 120/12 = 10.

P = 10/28 ≈ 0.357.

Answer: The probability that both balls are red is ≈ 0.357.