SOLUTION: certain class contains 60% of boys and 40% of girls, all aged between 17 and 27 years. It is known that 80% of young people of both sexes are under 21 years of age and that among g

Algebra ->  Probability-and-statistics -> SOLUTION: certain class contains 60% of boys and 40% of girls, all aged between 17 and 27 years. It is known that 80% of young people of both sexes are under 21 years of age and that among g      Log On


   

Question 1105385: certain class contains 60% of boys and 40% of girls, all aged between 17 and 27 years. It is known that 80% of young people of both sexes are under 21 years of age and that among girls, 10% are over 21 years.
a) a person is chosen and it is verified that he is under 21 years. What is the probability of being a girl?
b) a person is chosen at random. What is the probability of being a boy under the age of 21?
c) choose a boy at random. How likely is he to be less than 21 years old?
Answer by natolino_2017(77) About Me  (Show Source):
You can put this solution on YOUR website!
Let be the events A: The picked person is a Girl.
B: the picked person is under 21 or 21.
First P(A) = 40%. P(B) = 80%.
a) P(A/B) = P(A&B)/P(B)=(90%(40%))/(80%)=9/20.
b) P(A^c&B) = 60%(80%) = 12/25.
c) P(B/A^c) = P(B&A^c)/P(A^c) = (12/25)/60% =4/5.
#natolino_