SOLUTION: In a certain barnyard all the chickens are either red or black, 10% of the chickens are roosters. Half of the roosters are black. If a chicken is chosen at random, what is the pr

Algebra ->  Probability-and-statistics -> SOLUTION: In a certain barnyard all the chickens are either red or black, 10% of the chickens are roosters. Half of the roosters are black. If a chicken is chosen at random, what is the pr      Log On


   

Question 947658: In a certain barnyard all the chickens are either red or black, 10% of the chickens are roosters. Half of the roosters are black. If a chicken is chosen at random, what is the probability that it is both a rooster and is black?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
chickens are either red or black.
10% are roosters.
50% of roosters are black.
probability a chicken is both a rooster and black will be 10% * 50% = 5%.
for example:
assume 100 chickens.
10% are roosters.
that makes 10 that are rooster.
50% of the 10 are black.
that makes 5 of the roosters that are black.
you have 5 chickens out of 100 that are both black and a rooster.
5/100 = .05 = 5%.
probability that you randomly pick a chicken out of the group of chickens and that the chicken is both black and a rooster is 5%.