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 a 2 the first time and a 3 the second time.

Accepted Answer

hey everyone in this problem. We have a small cube with different colored sides, red, blue, yellow, green, brown and white. And strolled twice. And were asked what is the probability of having the color brown face up the first time? And white the second time. So let's start just by finding the probability of Rolling Brown on its own and the probability of rolling White on its own. Okay, so the probability of Rolling Brown will call it P. B. It's going to be well, we have one brown side and six total sets. Okay, so the probability of Rolling Brown, There's gonna be one in 6. What about for white? Well this is similar. Okay, probability of Rolling White. Again, we have one white side and six total side. So the probability of Rolling White is also one in six. All right. Now we want to find the probability of Rolling Brown the first time and white the second time. Now when we have this small cube, we raw it and we roll it. Once we roll it a second time, the outcome of the first rule doesn't affect the second room. Okay. It doesn't matter what color we roll the first time. When we roll it the second time, the probabilities are the same. Okay, you still have the same probability of getting red, blue, yellow, green, brown or white on the second role, no matter what you rolled on the first roll. Okay, that means that these are independent events. And if these are independent events then when we're looking at the probability of brown and white, it's just gonna be equal to the probability of rolling Brown times the probability of rolling white. Okay, so we're gonna have 1/6 times 6. Which is gonna give us a probability of 1/36. And so the probability of having brown face up the first time and white face up the second time is going to be d. one in 36. That's it for this one. Thanks everyone for watching. See you in the next video.