Question Video: Determining the Probability of the Union of Two Events Mathematics • 7th Grade

In a sample of 55 people, 28 of them have brown hair and 22 of them have blue eyes. 5 of them have neither brown hair nor blue eyes. What is the probability that a random person from the sample has at least one of these features.

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Video Transcript

In a sample of 55 people, 28 of them have brown hair and 22 of them have blue eyes. Five of them have neither brown hair nor blue eyes. What is the probability that a random person from the sample has at least one of these features?

If this is our sample, there’s a total of 55 people. 28 have brown hair, 22 have blue eyes, five have neither brown hair nor blue eyes. We’re looking for the probability that a random person from this sample has at least one of these features. That’s the probability that they have brown hair or blue eyes. But in order for us to solve this, we need to find out, are there any people with both brown hair and blue eyes in the sample?

If we add all three categories, the brown hair, the blue eyes, and the neither category, we get 55 people, the total from the sample. This tells us that there are no people with both brown hair and blue eyes in this sample. So, to find the probability, we would add 28 over 55 plus 22 over 55. 50 out of the 55 people have either brown hair or blue eyes. We can take this probability and simplify it by dividing the numerator and the denominator by five. And then, we would have 10 over 11.

The probability of selecting either a brown hair or a blue-eyed person is ten elevenths.

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