The probability of a flood in any given year in a region prone to...

Question

The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of a flood for three consecutive years?

Accepted Answer

Welcome back. I'm so glad you're here. We've got this strange flower that only blooms at night guaranteed to bloom once every month. And we want to know the probability of it blooming three consecutive nights in a row. While the first question we want to ask ourselves is are these independent events? If it blooms on the first night? Does that affect whether it blooms on the second night and if it blooms on the second night, does that affect whether it blooms on the third night and no, it doesn't. So they are independent events. So we recall that for independent events, the probability of the first event A and the second event B and the third event, see all occurring is going to be the probability of the first event times. The probability of the second event times. The probability of the third event. Great. So what are our probabilities here? Well, the probability of it blooming on any night is 1/30. I'm going to keep that as a fraction because it's more accurate. So the probability of it blooming For the first event, which is for the first night, that's 1/30. And the probability of it blooming that second night? Well that's still 1/30 because it's not affected by it blooming the previous night and the probability of the third event occurring that it blooms on the third night, that is still 1/30. So we've got 1/30 cubed and we can go ahead and plug that straight into a calculator, 1/30 cubed or 1/30 time's 1/30 times 1/ and we're going to get an answer and I'm going to convert this to a decimal because all our answers are in decimals, we're going to get an answer of 0.0. So four zeros there, 37037, which matches with answer choice? A well done, we'll catch you on the next one.