Question

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An experiment consists of rolling a die and then flipping a coin.

The following tree diagram shows the possible outcomes.


A tree diagram in which a center point branches to numbers 1 through 6, which each branch to an H & T.

© 2018 StrongMind. Created using GeoGebra.


What is the probability of rolling an even number or flipping a tail?

Enter your answer as a reduced fraction, like this: 3/14

Answer 1

Outcomes of rolling an even number are 2, 4, and 6. Outcomes of flipping a tail are T.

So, the probability of rolling an even number or flipping a tail is the sum of the probabilities of rolling an even number and flipping a tail, minus the probability of rolling an even number and flipping a tail (because this outcome is counted twice):

P(even or tail) = P(even) + P(tail) - P(even and tail)

P(even) = 3/6 (since there are three even numbers out of six possible outcomes)

P(tail) = 1/2 (since there is one tail out of two possible outcomes)

P(even and tail) = 1/6 (since only the outcome of rolling a 2 and flipping a tail satisfies both conditions)

Therefore,

P(even or tail) = 3/6 + 1/2 - 1/6 = 7/12

So, the probability of rolling an even number or flipping a tail is 7/12.