Probability of compound events

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TACHS Math › Probability of compound events

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When rolling a fair six-sided die and flipping a fair coin, what is the probability of rolling either a or a and getting heads on the coin flip?

$\frac{1}{6}$

$\frac{5}{6}$

$\frac{1}{4}$

$\frac{1}{8}$

Explanation

Recall what a probability is:

$\text{Probability}=\frac{\text{Number of desired outcomes}}{\text{Total number of outcomes}}$

Start by finding the probability of rolling either or on a die. Since there are a total of different outcomes, and we only want these two, the probability must be $\frac{2}{6}\text{, or }\frac{1}{3}$ .

Next, find the probability of getting heads on a coin flip. Since we only want heads and there are only possible outcomes on a coin flip, the probability of getting heads is $\frac{1}{2}$ .

Since the question wants the probability of both events occurring, you must multiply the probabilities together.

$\text{Probability of rolling 1 or 6 AND probability of flipping heads}=\frac{1}{3}\times \frac{1}{2}=\frac{1}{6}$