There are 7 red and 8 green balls in the urn. 4 balls are taken from the urn at the same time.

There are 7 red and 8 green balls in the urn. 4 balls are taken from the urn at the same time. What is the probability that these balls are red?

The total number of outcomes when choosing 4 balls out of 15:
n = C (15,4) = 15! / (4! (15 – 4)!) = 12 13 14 15 / (1 2 3 4) = 1365.
The number of ways to get 4 red balls out of 7.
C (7.4) = 7! / (4! (7 – 4)!) = 5 6 7 / (1 2 3) = 35.
The number of ways to remove 0 green balls out of 8.
C (8.0) = 1.
Number of favorable options:
m = C (7.4) C (8.0) = 35 1 = 35.
Chance to take out 4 red balls:
P = 35 1/1365 = 0.026.
Answer: 0.026.