Two Events (A and B)
About this exercise
The probability that two independent events both happen.
Example problems
A few of the problems this exercise asks. The printable worksheet holds ten fresh ones.
- P(A) = 1/6 (even number) P(B) = 2/5 (blue ball) Find P(A and B) = ?
- P(A) = 1/5 (even number) P(B) = 4/6 (rolling 6) Find P(A and B) = ?
- P(A) = 1/2 (even number) P(B) = 1/2 (blue ball) Find P(A and B) = ?
- P(A) = 1/6 (even number) P(B) = 3/6 (consonant) Find P(A and B) = ?
Try it yourself first — open a section below only if you get stuck.
How to solve it
Multiply the two probabilities. Multiplying always shrinks the result, which matches the fact that asking for both is harder than asking for either.
Worked example
An even number on a die together with tails on a coin is one half times one half, which is one quarter.
Common mistake
Adding the probabilities. Addition answers a different question — the chance that one or the other happens.