Combined Probability

When you have two or more events happening in a question:

  • Break the question down into a sequence of separate events
  • Find the probability of each happening
  • Apply the AND/OR rule

P(Both Events Happen) = AND Rule

P(A and B) = P(A) x P(B)

So if you need to find the probability of Event A and Event B happening you multiply their separate probabilities together.

Example: Bag one contains 6 balls, 3 of which are red. Bag two contains 10 balls, 4 or which are red. What is the probability a red ball is picked from both bags?

P(red from both bags) = 3/6 x 4/10 = 0.2

P(At Least One Even Happens) = OR Rule

P(A or B) = P(A) + P(B)

So if you need to find the probability of Event A or Event B happening you add their separate probabilities together.

Example: A spinner has a green, red and blue side. The probability of it landing on each side is:

Green – 0.4
Red – 0.5
Blue – 0.1

What is the probability of it landing on green or blue?

P(lands green or blue) = 0.4 + 0.1 = 0.5