Problem 43 Medium Difficulty

Q and R are independent events. P(Q) = 0.4 and P(Q AND R) = 0.1. Find P(R)

Answer

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Video Transcript

Hi, We're looking at Question 43. It tells us that Q and our independent events and that's gonna be key to be able to answer a question. And then it also tells us that the probability of Pew is equal to 0.4, and the probability of Q and R is equal to 0.1. And it's asking us to find the probability of our. So we need to remember to key things to be able to do this. The first is our test for independence. And remember, the test for Independence says that if the probability of a given B is equal to the probability of a, then are two events are independent and then the other piece that we need is that definition or the formula that we used to find the probability of a given B and the probability of a given B is equal to the probability of A and B all over the probability of the So we're going to put those two pieces together to be able to solve this. Since we want to find are we wanna have this first definition bee, the probability of our equal to something so that means that this side we wanna have the probability of our given. Q Um, and that's so that we'll be able to find the probability of our and then on this left side we can substitute our formula or definition for the probability. And that's the problem. You are in Q or Q and R SE thing, um, over the probability of cute. And that's equal to the probability of our. And since they gave us the two pieces we need to be able to substitute into the left side of this equation, we can substitute in the Q and R, which is the same Zarin Q is 0.1, and then 0.4 was probably a pew, and that's equal to the probability of our. And when we put that in our calculator and do 0.1 divided by 0.4, we end up with 0.25 which is our probability for