A bag contains 5 balls two balls are drawn at a random and found to be red what is the probability that all balls are red?

Answer 1

The probability that all balls are red is 0.50 or 50%.

EXPLANATION

Suppose there are 4 boxes with 5 balls each.

Box A has 2 red balls.

Box B has 3 red balls.

Box C has 4 red balls.

Box D has 5 red balls.

The probability of drawing at random 2 red balls for each box is:

Box A; P(2 red balls) = (2/5)∙(1/4) = 2/20 = 1/10

Box B; P(2 red balls) = (3/5)∙(2/4) = 6/20 = 3/10

Box C; P(2 red balls) = (4/5)∙(3/4) = 12/20 = 6/10

Box D; P(2 red balls) = (5/5)∙(4/4) = 20/20 = 10/10

Now, suppose we do the drawing of 2 balls experiment 10 times on each box

giving a total of 40 experiments. The probabilities calculated above are the

"expected" results, that is; out of the 40 experiments (drawing of 2 balls), two

red balls resulted:

1 time came from box A

3 times from box B

6 times from box C

10 times from box D

Notice that from the 40 experiments, 20 result in 2 red balls.

From here we have that when drawing 2 red balls the probability that it came

from a box containing 2 red balls (box A), 3 red balls (box B), 4 red balls (box C)

or 5 red balls is:

P(A) = 1/20 = 0.05 = 5%

P(B) = 3/20 = 0.15 = 15%

P(C) = 6/20 = 0.30 = 30%

P(D) = 10/20 = 0.50 = 50%