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Combined Events: AND

For independent events, the probability of A and B both happening is P(A) multiplied by P(B).

Both Happening

Example 1 — AND with a coin and a die

A coin is flipped and a die is rolled. Find P(heads AND rolling a 6). 1 These are independent events 2 P(heads) = \frac{1}{2}, P(rolling a 6) = \frac{1}{6} 3 Multiply: \frac{1}{2} \times \frac{1}{6} Answer: \frac{1}{12}

Example 2 — AND with two spins

A spinner has P(red) = 0.3 . It is spun twice, independently. Find P(red, then red). 1 Multiply the probability by itself: 0.3 \times 0.3 Answer: 0.09

Practice

Two fair coins are flipped. Find P(both land heads).

Your answer

Both Happening

Example 1 — AND with a coin and a die

A coin is flipped and a die is rolled. Find P(heads AND rolling a 6). 1 These are independent events 2 P(heads) = \frac{1}{2}, P(rolling a 6) = \frac{1}{6} 3 Multiply: \frac{1}{2} \times \frac{1}{6} Answer: \frac{1}{12}

Example 2 — AND with two spins

A spinner has P(red) = 0.3 . It is spun twice, independently. Find P(red, then red). 1 Multiply the probability by itself: 0.3 \times 0.3 Answer: 0.09

Practice

Two fair coins are flipped. Find P(both land heads).

Your answer