# A box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that, one is red and the other is green? - Mathematics and Statistics

Sum

A box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that, one is red and the other is green?

#### Solution

Total number of balls = 10 + 15 = 25

To find the probability that one ball is red and the other is green, there are two possibilities:

First ball is red and second ball is green.

OR

First ball is green and second ball is red. From above, we get

P(First ball is red and second ball is green) = 1/4

Similarly,

P(First ball is green and second ball is red)

= (""^15"C"_1)/(""^25"C"_1) xx (""^10"C"_1)/(""^24"C"_1)

= 15/25 xx 10/24

= 1/4

∴ Required probability

= P(First ball is red and second ball is green) + P(First ball is green and second ball is red)

= 1/4 + 1/4

= 1/2

Concept: Event and Its Types
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