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 no flooding for four consecutive years?

Accepted Answer

Welcome back. I'm so glad you're here. We've got a bit of a riddle here. Tardy tam is often lee never early, seldom on time. We want to know the probability of him being on time monday through friday. So on any day on monday and on Tuesday and so on, we've got three choices. Tardy tam could be late, tardy tam could be early or tardy tam could be on time. Were given that Tardy Tam is late 35% of the time or 0.35 and we've got to figure out early and on time. Well, since those are three possibilities, they're all going to add up to one or 100% of the time and were given another clue that early occurs. Never so Tony Tam is early 0% of the time. Never. So for on time that's going to be the total 100% or 1 -35% or 0.35. So Tardy Tim is on time 0.65 or 65% of the time. Well that's not looking too bad. Getting there better than half of the time. But now we're asking for monday and Tuesday and Wednesday and thursday and friday. So we've got to figure out the probability for all of those and we recall from previous lessons that we've got a formula we can use for this but we need to know is this are these independent of each other these events? If tardy tam is on time on monday. Does that affect tardy tam being on time on Tuesday? Well it doesn't they are independent. So what we're going to use is we'll use the probability of a. That's being on time on monday and be that's Tuesday and see and D. And E. So those are the rest of the days of the week, monday, Tuesday Wednesday thursday friday. The probability of all of those things being on time on all of those things is going to be the probability of a times the probability of B. Times the probability of c. Times the probability of D. Times the probability of E. So that's the formula that we recall and now we can just fill it in probability of being on time on Monday 0.65 probability of being on time Tuesday 0.65 probability of being on time on Wednesday 0.65 Probability of being on time Thursday 0.65 probability of being on time Friday 0.65. So all together we multiply those and we will get that tardy tam is on time every day of the week with a probability of 0.1160 or about an 11% chance. The tardy tam is going to be on time every day during the week. Well that's slightly different. So we look at our answer choices that matches with answer choice C. Well done. We'll catch you on the next one

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The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of no flooding for four consecutive years?