Events A and B are two independent events. The probability of event A occurring is 20%, and the probability of event B occurring is 33%. What is the probability of events A and B occurring?

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Video Transcript

So in this question, we're told that events, a and b, are 2 independent events and that the probability of event occurring is 20 per cent and the probability of event b occurring is 33 percent. What we are asked for is the probability that both of these events occur. Okay, in order for us to be able to do this question, we need to understand what independent events are. So independent events are events that occur, irrespective of whether other events occur right. So flipping heads on a coin isn't going to affect what happens the next time we flipped the coin right. So that's 1 thing about them and the second thing about them is: we have a little rule. We can use 1 talk about them right where we say that if events a and b are independent events, then the probability of events, a and b occurring is the same thing as the probability of a times the probability of b. So keeping that in mind, let's look back at our question. We'Re told that we actually know were given a probability of a and a probability of b right probability of a is 20 percent or 0.2 and the probability of b is 33 percent or 0.33 okay. So now we're asked for the probability that both of these events occur and since they're independent, we can just multiply them together so 0.2 times 0.33. Okay, and when you do that what you're going to get is 0.066. So that's the probability of both events, a and b occurring, and that wraps up our question. I hope it helped you out.

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