In Exercises 49–52, a single die is rolled twice. Find the probab...

Question

In Exercises 49–52, a single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.

Accepted Answer

everyone in this problem we have a small cube with differently labeled sides, A, B, C, D, E and F. And it's rolled twice. And we are asked to calculate the probability of having a vowel letter face up the first time in a consonant the second time. So let's start by finding the probability of having a vowel letter on its own. The probability of having a continent on its own and go from there. Okay. So the probability of having a vowel. What is this? Well how many vowels do we have? We have a. Which is about all. We have E. Isabel. So we have two possible values. Oh sorry to possible vowels out of 123456 total sides on our dais there are Cube. So this gives us a probability two and 6 or 1/3. So that's the probability of getting a vowel. Similarly the probability of getting a consonant. Well how many continents? We have? Two vowels and 1234 consonants. Okay. Out of six Total size. Which gives us a probability of rolling consonant of 2/3. So we know the probability of getting a vow. We know the probability of getting a continent on their own. What about the probability of getting a vowel the first time in a continent? The second time. So that's the probability of a vowel and a consonant. Okay. That's what we want to find. Now when we roll the first time we get either a vowel or consonant and then we roll the dice the second time. Okay these are independent events. Okay. It doesn't matter what we roll the first time. The second time we still have the same probabilities. Okay if we roll an A. The first time we have the same probability of getting a B C. D. E. Or F. The second time. The first the outcome of the first event doesn't change the second event. So that means that these are independent. And if they're independent then when we have the probability of one and the other we could just multiply them together. So we get the probability of V. Times the probability of C. Well this is gonna be 1 3rd times two thirds. I'm just gonna be to over nine. And so the probability of rolling a vowel first and then a consonant is going to be D. 2/9. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 49–52, a single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.

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