# Conditional probability given a pdf

First time posting here. I'm having trouble conceptualising the following question. Any tips or pointers would be greatly appreciated. Direction to a solution to a similar problem would also be fantastic - i'm not so much looking for a solution, as how to go about solving this kind of problem.

5 weight lifters work out each day. The risk of injury within 5 hours of working out, X, varies from day to day according to the pdf f(x) ={ 10x, 0 ≤ x ≤ 0.1 { 15/7(1−x), 0.1 < x ≤ 1

Derive a formula for the conditional probability of exactly 2 injuries (2 people) within 5 hours of exercise among the 5 weight lifters on any given random day (number of injuries follows a Binomial distribution)

Many thanks.

• All you are asked is to write down the Binomial distribution formula: there doesn't seem to be much "conceptualization" required for this kind of plug-in textbook question. – whuber Jun 9 '18 at 18:19
• I came up with the following Let Y = the number of deaths. P(Y=2|X=x)=(5!/2!3!) X^2 (1-X)^3 How am I looking? :) – shrub Jun 10 '18 at 7:40
• You're doing well, but pay attention to the details: "X" and "x" mean different things. The first names a random variable whereas the second names a number. The conditional probability, being a probability, must ultimately be a number. – whuber Jun 11 '18 at 13:22