Inside a box, there are 16 marbles in which 7 are red and the rest are blue. 16 people that consists of 11 males and 5 females lined up to randomly pick one marble at a time. The females occupied the 3rd, 4th, 8th,9th, and 14th spot and the males occupied the rest.
Assuming that there is no replacement, what is the probability that all female would have red marbles?
Please HELP!!! Thank you <3.
The only thing 'hard' about this problem is recognizing that most of the information given is irrelevant. The "a-priori" probability that a given person has a red marble is independent of their place in line. It is sufficient to imagine that the females are first in line. The probability that the first female in line gets a red marble is 7/16, the probability that the second female gets a red marble is (7-1)/(16- 1)= 6/15, the probability the third female gets a red marble is (6- 1)/(15-1)= 5/14, fourth 4/13, fifth 3/12. The probability all 5 females get red marbles is