In Exercises 45-46, it is equally probable that the pointer on th...

Question

In Exercises 45-46, it is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number less than 6.

Accepted Answer

Hello. Everyone in this video, we're going to be looking at this practice problem where we want to find the probability that a shaft on a ferris wheel that has 12 seats lands on a vowel letter or a letter labeled A through F. So in this case, let's get started by drawing this ferris wheel. So the ferris wheel has 12 seats. So I'm gonna go ahead and draw a circle to represent my ferris wheel and I'll draw little circles to represent the seats on the ferris wheel and I'll try to do them as equidistant as I can. And I'll make sure that there's 12 seats on here and the 12 seats are labeled A through L. So I'm gonna go ahead and start by labeling my bottom one A. And will continue through the alphabet until I get to L. So I'll have a B c, d, e, f, G, H, I, JK and finally L. And you can see that on my ferris wheel, I've drawn 12 seats and I'll go ahead and number them. So for this problem, I care about finding where this shaft and I'll go ahead and draw a shaft pointing north. I care about the probability of the shaft landing on a vowel letter or the letters A through F. So let's go ahead and figure out the possible outcomes first. So the number of total outcomes Is 12 because there's 12 seats. So the shaft could land on any one of those 12 seats and the number of favorable outcomes is the outcomes that I want. So in this problem I'm looking for the vowel letters or the letters A through F. So I'm going to go ahead and count first the letters A through F. So That's 1, 2, 3, 4, 5, 6 seats. For the letters labeled A through F. And then you can see that I is also a bell. So that's seven seats. That would mean favorable outcomes. So in order to find the probability of the shaft landing on the vowel letters or the letters A through F, which I have determined to be my favorable outcomes, I need to divide the number of favorable outcomes by the number of total outcomes. And because I've already determined both of those numbers, you can see that in my numerator, I'll have seven, the number of favorable outcomes. And in my denominator I'll have 12. The number of total outcomes. So seven out of 12 becomes my probability of landing on a vowel letter or a letter labeled A through F. And this becomes my final answer. And you can see that that aligns with answer choice B. Hopefully this video helped and see you next time