Recall the formula for the probability of compound events. Calculate each of the probabilities from the formula separately.
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Practice makes perfect
We are told that we can win concert tickets from the radio station if we call after the song of the day is played or if we correctly answer a trivia question. We want to find the probability that we will miss the song of the day or the trivia question if we start listening to the radio at 7:20AM. This will be a probability of compound events. Recall how we calculate it.
P(AorB)=P(A)+P(B)-P(AandB)
In our case event A will be missing the song of the day, and event B will be missing the trivia question. We know that the song is played between 7:00AM and 7:30AM. This gives 30 minutes of total time when the song can be played. Since we start listening to the radio at 7:20AM, there are 20 minutes in which we could miss the song.
P(A)=20/30= 2/3
Additionally, the trivia is asked at a random time between 7:15AM and 7:45AM. This gives 30 minutes of total time when the question can be asked. Since we start listening to the radio at 7:20AM, there are 5 minutes in which we could miss the trivia question.
P(B)=5/30= 1/6
Now consider the event of missing both the song and the trivia question. Note that these events are independent, since missing the song does not affect missing the trivia question in any way. Recall that to calculate the probability of two independent events we need to multiply the probabilities of both events.
