"Using the Multiplication Rule In Exercises 19-32, use the Mul...

Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

27. Blood Types The probability that a person of Asian descent in the United States has type O+ blood is 39%. At random, six people of Asian descent in the United States are selected. (Source: American National Red Cross)

a. Find the probability that all six have type O+ blood."

Accepted Answer

Hi everyone, I'm glad to have you back. The next problem says in an office 8 employees bring lunch from home and 4 order takeout. If two employees are randomly selected without replacement to join a wellness program about healthy eating, what is the probability that both bring lunch from home? A 0.25, B 0.51, C, 0.42, or D 0.60? So in this case, we need to start by thinking about, we have 2 events, and they're dependent, because there's no replacement happening. So we'd say, what is the probability? Of the first amount, so probability of. Employee number one. Bringing lunch. So we know that 8 employees out of 12, because we have 8. Bringing lunch and 4 ordering takeout, we'll say N equals 12 employees total. So the probability of one of them bringing lunch would be 8, the number that brought lunch. Divided by 12, the total number or 8 12th. And then my second event would be the probability. Of the 2nd. Employee bringing lunch as well. So remember that now the overall odds have changed, because I have removed. One employee. That brings their lunch. So now, how many employees in our whole pool would bring lunch, and that is 7. So 7 goes in the numerator there. Otsy 7 And then in the denominator, we no longer have 12 employees, we removed one. So now we have 11 employees. So the probability for the second bringing lunch. Oops, we got an H on lunch there. Equals 7 11th. So now our question saying, what is the probability that both Bring lunch. And since we have the probability of 2. Events, we multiply these probabilities. So that will be the probability that the first ring's launch, so 8 12th. And then multiply that by the probability that the second brings lunch, which will be 7 11th. So when we do that multiplication. We will end up with Approximately, we'll round that off, 0.424. So, when we look at our answers, they're rounded off to the hundreds place, and this corresponds to choice C 0.42. So again, we were asked to calculate, we had 2 dependent events because we were taking an employee out of the pool without replacement, and calculating the probability that if 2 employees are removed to join a healthy eating program, what is the probability that both bring lunch from home when we know from our original pool how many brought lunch from home, how many ordered takeout? So we calculated the probability that the 1st 1 brought lunch, the probability the 2nd brought lunch. And then multiplied those probabilities to to get the probability of both brought lunch. And our answers to C 0.42. See you in the next video.

Key Concepts

Multiplication Rule of Probability

Independent Events

Probability Calculation

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