Video: Using the Addition Rule to Determine the Probability of Union of Two Events

A small choir has a tenor singer, 3 soprano singers, a baritone singer, and a mezzo-soprano singer. If one of their names was randomly chosen, determine the probability that it was the name of the tenor singer or soprano singer.

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Video Transcript

A small choir has a tenor singer, three soprano singers, a baritone singer, and a mezzo-soprano singer. If one of their names was randomly chosen, determine the probability that it was the name of the tenor singer or the soprano singer.

The choir has one tenor, three sopranos, one baritone, and one mezzo-soprano. If we let them be mutually exclusive, that means the tenor would not also be the baritone. We would say there is six total people. We want to know the probability of tenor or soprano. And because they’re mutually exclusive, we can just add these values together, the probability of a tenor and the probability of a soprano.

Since there’s only one tenor, the probability of randomly selecting that person is one out of six. And since there are three sopranos, the probability of randomly selecting their name would be three out of six. Together, that’s a probability of four-sixths, which can be reduced by dividing the numerator and denominator by two. And that means the probability of randomly selecting a tenor or a soprano is two-thirds.

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