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Numerade Educator

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Problem 56 Medium Difficulty

Use the following information to answer the next four exercises. Table 3.15 shows a random sample of musicians and how they learned to play their instruments.
TABLE CANNOT COPY

Find P(musician is a female OR is self taught).

Answer

0.7

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Video Transcript

Hi. We're looking at the question that I asked about the probability of musician is a female or is self taught. And this one's a little more challenging because we've got a look at the probability that they're female, um, and self taught as well, a cz probability of just female and just sell thought. So remember, we need to find the probability that they're female, something F for female, plus the probability that they're self taught and I'll put S t for self tart. And then we have to subtract the probability that they're female and self taught because we don't want a double count on those people because they wouldn't actually be in the in the study twice. And so for answer the probability that the student is female. In general, you take the female column and follow it to the far right and get 72 plus the probability that they're self taught. So we find the self top column and follow that down to 31 and then subtract the probability that they're both female and self taught, which is finding that row and column and where they need, which is 12. So that means that we have a total of 91 students who are female or self taunts. And then we can divide that by the total in the whole table, because the 91 is our favorable outcomes. And remember, probability is favorable outcomes divided by possible all possible outcomes. And so 91 is our favorable outcomes and one thirties or possible outcomes. So we end up with 0.7. Thank you.