In Exercises 1–10, use the data in the accompanying table and ...

Question

In Exercises 1–10, use the data in the accompanying table and express all results in decimal form. (The data are from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education Resources Information Center, Paper 399519.)

Both Lefties If two of the study subjects are randomly selected with replacement, find the probability that they both write with their left hand.

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Both Lefties If two of the study subjects are randomly selected with replacement, find the probability that they both write with their left hand.

Accepted Answer

Welcome back everyone. In a survey conducted at a local high school, students were asked about their preferred learning style. The results were as follows. If two students are randomly selected with replacement, what is the probability that both prefer auditory learning? For this problem, let's first of all identify the probability of choosing a student that prefers auditory learning. So let's define P of A and we know that we're looking for a ratio between two numbers. Now what is the total number of outcomes that we are going to use in our denominator? Well, it is going to be the total number of students. We have to add 120. 200 180. And 300. So the total number of students is 800, and that's the denominator of our fraction in the calculation of the probability. We also need to identify the numerator. Our numerator M corresponds to the number of favorable outcomes, so we're only looking at the students who prefer auditory learning, and that would be the sum between 180 and 300, which is equal to 480. So the probability of choosing a single student who prefers auditory learning. is equal to. 480 divided by 800 or 35, right, because both the numerator and the denominator are divisible by 160. And now what we want to do is identify the event B. Which corresponds to choosing two students with replacement. That prefer auditory learning. We know that choosing the first student. Corresponds to 3/5. In terms of probability, and now we have to apply the multiplication rule for independent events because we're observing a selection with replacement, the probability of choosing another student. Who prefers auditory learning is going to be the same, meaning we're multiplying by 3/5. So essentially we're evaluating 3/5 multiplied by 3/5, which is 9 divided by 25. So that would be our final answer to this problem. Thank you for watching.

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Key Concepts

Probability

Independent Events

Replacement in Sampling

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