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 two years in a row?

Accepted Answer

Welcome back. I'm so glad you're here. We've got a superhuman here and their superpower. Well they gathered too much conductive power and get struck by lightning more than the average human does. Well that's I guess the superpower. And so now the probability of them getting struck by lightning is one out of 100. And we want to know the probability of being struck four times in a row. So the first question we ask ourselves are these independent events. If she is struck by lightning once, does that affect whether she's going to be struck by lightning again? Nope, these are independent of each other. So we recall from previous lessons that when we have the probability of event A. And the probability of event B. And the probability of event C. And the probability of event D. So those are the four events being struck by lightning four times and those are all independent of each other. Then we know that we can take the probability of event A times the probability of event B. Times the probability of events C. Times the probability of event D. So the probability of event a. That first lightning strike, that is 1/100. The probability of event B getting struck again, it's still 1 100. It's not affected by the first one probability of events. See getting struck again, still 1 100 Not affected by the previous strikes and D same thing. That's 1 100th Not affected by the previous strikes. So now we take those four and we multiply them together. So we've got 1/100 to the fourth. There are many different ways to solve this at this point. You can put that into a calculator and or you could count how many zeros are we moving this um decimal point, How many is this moving over and you'll get Many different ways to get this same answer of 0. Zeros. And then R1. Because the decimal place has moved over eight Places to the left or in scientific notation one times 10 to the -8. As we said, it moved eight decimal places to the left, we look at our answer choices and that matches answer choice. C. While done, we'll catch you on the next one.

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 two years in a row?

Key Concepts

Probability Basics

Independent Events

Multiplication Rule of Probability

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