Probability practice questions #3:

1. If there is a 40% chance that it will rain, there is a 60% chance that it will not rain (100%-40%=60%)

2. If I have a bag with 5 red and 3 blue marbles, and I pick two out (one and then the other,without replacing the first)

These are best done by multiplication:

• What is the probability I will get two red marbles? (5/8)(4/7)=20/56=5/14

  Note that 5/8 is the probability of getting a red the first time, after which there are 4 red out of 7 total marbles left, for a probability of 4/7

• What is the probability I will get two blue marbles? (3/8)(2/7)=6/56=3/28
• What is the probability that I will get one red and one blue?

  You can do this two ways: add together red then blue and blue then red: (5/8)(3/7)+(3/8)(5/7)=(15/56)+(15/56)=30/56=15/28
  OR you can subtract the probabilities of RR and BB from 1 (since one of each is the only other possible outcome):
  1-(5/14)-(15/28)=(56/56)-(20/56)-(6/56)=30/56=15/28

You can show all of these together on a tree diagram: