# Thread: Stuck on probability problems

1. ## Stuck on probability problems

At a high school, 40% of the students are in a sport. 65% are in a club. What is the probability that a student selected at a random participates in a sport? In a club? IS the probability of both occurring more or less likely than either one occurring?

and...

A deck of cards has 52 cards. 13 each of 4 different suits. The hearts and diamonds are red and the spades and clubs are black. What is the probability of drawing a heart? If you draw a heart and not replace, what is the probability of drawing it again? If you draw 3 times, replacing each card, what is the probability of drawing 3 hearts? Construct tree diagrams of each the experiments.
________________
Answers would work but what I need most is how to solve them. Thanks!

2. A student selected at random participating in a sport is exactly the percentage you gave: 40%, likewise for a club: 65%. To find the probability of a student being in both a club and a sport you multiply the probabilities (.4*.65) = .26 = 26%. If you know that 26% are in both, you know that (40-26=14) 14% are only in sports, and (65-26=39) 39% are only in club, therefore 26% are in both and (14+39=55) 55% are in either one so it is less likely a student is in both than either one.

The probability of drawing a heart is: # hearts/ #total = 13/52 = 1/4 = 25%. If you draw a heart and don't replace it, the odds of drawing another heart are now 12/51 = .235=23.5%. If you draw 3 times, replacing each time, you have the same probability each time so it is (13/52)*(13/52)*(13/52) = (.25^3) = .016 = 1.6%. You can construct a tree diagram by putting each of the suits as a branch for the first try, then each of the suits off of each branch for the 2nd and 3rd tries.

3. For the first one, draw a Venn diagram, with one circle representing students in clubs and one representing students that play a sport. Assume that there are 100 students in total. You have 40 students doing some sport and you have 65 students in a club. How many students are both in a club and doing a sport? (Hint: let the number of people participating in both activities be x)

For the second one, since there are 13 hearts in a deck of 52 cards, the probability of drawing a heart is 13/52=1/4. I'll let you continue from here. Note that the probability of two independent events occurring is the product of their individual probabilities. For example, the probability of drawing 2 kings in a row is (4/52)*(3/51). 4/52 for the first king, and 3/51 for the second king.