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

Question

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

23. Celebrities as Role Models In a sample of 1103 probable voters, three out of four say they would like entertainers to address social and political issues. Two probable voters are selected at random. (Source: The Hollywood Reporter)

a. Find the probability that both probable voters would like entertainers to address social and political issues.

Accepted Answer

Welcome back, everyone. In a survey of 900 registered voters, 5 out of 6 say they support stricter environmental regulations. If two voters are picked at random without replacement, what is the probability that both support stricter environmental regulations? A says it's about 0.461. B about 0.529. C about 0.638, and D about 0.694. Now, in this problem, let's first let A OK, be the event. That the first order. OK, the first voter. Is a supporter of. Is a supporter. Uh Stricter environmental regulations, OK. So let's first define our events. And then, if that's the case, let's let B, so I'm just gonna, it's basically going to be similar to this statement, but no, let's let B, OK. Uh be Be the event that the 2nd voter, not the 2nd voter. Is a supporter of stricter environmental regulations, OK? Then what would be the probability that both support stricter environmental regulations? Well, to help us figure that out, we can use the multiplication rule, and no notice here. That from our survey, OK, if the second voter is a supporter of stricter environmental regulations, OK, then the fact that the first supported it as well will affect the probability of the second. So this probability that be given A is going to be conditional. OK, so by the multiplication rule of events. Uh, for dependent events, the probability that both support the regulations a intersect B is going to be equal to the probability of a multiplied by the probability of B given A. So we need to figure out both of these probabilities to find the probability they both support the regulations. Now, let's first start with the probability of A. What's the probability a first voter supports these regulations? Well, not in our problem statement we were told that 5 out of 6 say they support stricter environmental regulations from a survey of 900 registered voters. OK, so that means then that the number who support the regulations. OK, for our first scenario is going to be equal to 5/6 of 900, which is 750, and that means since there are 750 voters who support stricter environmental regulations, then the probability of event A will be equal to 750 the number of successes divided by 900, the number of registered voters, OK. Now, given that the first, the first voter chosen was a supporter, there are no 749 supporters left out of 899 voters. OK? So if the probability of B given A is the probability that the second voter is a supporter given the first voter is also one, then that means the probability of B given A will be equal to. 749, 1 less than 1 less success, OK, divided by 899. 1 less voter because we've already removed that successful first voter from our uh our list. So now, since we have the probability of a and the probability of B given A, this would mean then that the probability of a intersect with B is going to be equal to 750 divided by 900. Multiplied by 749 divided by 899. That is equal to 3,745 divided by 5,394, which would be approximately 0.694. So the probability that both support stricter environmental regulations is about 0.694. Therefore, D is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

��app

Key Concepts

Multiplication Rule of Probability

Independent Events

Probability Calculation

Watch next