PLEASE HELP-MATH-PROBABILITY PROBLEM?

Question

ok this is my question:

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend

are among the 100 students, what is the probability that

(a) you both enter the same section?

(b) you both enter the different sections?

please explain every step clearly because this has been bugging me all day..thanks: )

Answer 1

You have to think about this problem in reverse, (I know it sounds strange).

Suppose the weatherman said there was a 80 percent chance of rain tomorrow.

You would KNOW that there is a 20% chance of NO RAIN, right?

Same logic applies here.

Probability that you and your friend are together in the smaller section:

P(together in smaller section) = .40 * .40 = .16

Probability that you and your friend are together in the larger section:

P(together in larger section) = .60 * .60 = .36

Probability that you and your friend are together in either section:

P(together in either section) = .36 + .16 = .52 or 52%

Probability that you and your friend are separated:

P(separated) = 1.00 - .52 = .48 or 48%

Good luck in your studies,

~ Mitch ~