SOLUTION: The probability tha a student does his homework 0.1, if he goes out with friends,and 0.6 if he does not go out with friends.the probability that a student goes out with friends is

Question 1077087: The probability tha a student does his homework 0.1, if he goes out with friends,and 0.6 if he does not go out with friends.the probability that a student goes out with friends is 0.75.What is the probability that the student does his homework?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
probability that he does his homework given that he goes out with his friends is .1

probability that he does his homework given that he does not go out with his friends is .6

probability that he goes out with his friends is .75.
probability that he does not go out with his friends is .25.

probability that he does his homework is equal to .75 * .1 + .25 * .6 = .225

since probabilities and percentages are related, you can look at this as a percentage type problem.

suppose he has 1000 homework assignments.

75% of the time he goes out with his friends = 750 times.
25% of the time he doesn't go out with his friends - 250 times.

he does his homework 10% of the 750 times = 75 times.
he does his homework 60% of the 250 times = 150 times.

the total number of times he does his homework is 225.

225/1000 = .225 = 22.5% of the time.

probability that he does his homework is equal to .225 = 22.5%.

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