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Develop a simulation using a TI- $83 / 84$ Plus calculator, Statdisk, Minitab, Excel, or any other suitable calculator or computer software program. Simulating the Shaq Refer to Exercise $7,$ which required a description of a simulated free throw by basketball player Shaquille O'Neal. a. Repeat the simulation five times and record the number of times that the free throw was made. Is the percentage of successful free throws from the simulation reasonably close to the value of $0.527 ?$ b. Repeat part (a) until it has been conducted a total of 10 times. Record the proportion of successful free throws in each case. Based on the results, would it be unlikely for Shaquille O'Neal to make all of five free throws in a game?

What are odds? Let's say I haven't Event E and I want to find the odds in this favor. So how do I do that? The formula for that is count off. Favorable outcomes. Count off favorable outcomes. Count off favorable outcomes upon count off. Unfavorable outcomes, Unfavorable outcomes, unfavorable outcomes. Okay, now odds in the favor of event A r n by M. R n is to him, or I can write this as this can also be returns and buy em. Okay, Now there are only two possibilities. Either they will happen, which means in any cases, it is happening or they will not happen. Which means that in any case, is it is not happening. So what is my total sample size? My total sample size is going to be in pleasant is going to be n plus and this is my total sample size. What is the probability off a probability off a is number off favorable outcomes that is end upon total number of outcomes, which happens to be in place. Um, this is the difference between odds and probability. Okay. In arts, the formula is the number off favorable outcomes upon the number off unfavorable outcomes. But in probability, the formula is number off favorable outcomes that his end upon total number off outcomes. So instead, off em over here, I will write n plus m. This is what we wanted to prove. We have done it. Now let us move on the part B. What are they saying in part B? Okay, the odds off making a sale on a single call. Our 2 to 15. So these are my odds. 2 to 15 are my odds, right? So what is the probability off a successful call? The probability off a successful call is going to be. This is favorable outcomes. And this is unfavorable outcomes. What is probability? Probability is going to be favorable upon favorable plus unfavorable. So it is going to be too by 17. This is my probability here, off a successful called Moving onto Part C. In fact, see, a sports announcer says that the odds a basketball player will make a free throw short are 3 to 5. Okay, so now my odds are threes to five and I will find the probability that the shot will be made. This is favorable. This is unfavorable. So the arts currently look against him. So what is the probability Favorable upon unfavorable Plus Favorable. So this is going to be three of all upon three plus five, which is eight. So this is my probability, in this case, off making a shot. And this is my answer.

Well that's what we're talking about. The difference between odds and probability. For example if the odds of a recurring or 2-1. What that tells us is that the probability This to over three and the three came from some of those two values there. Now here in the first part we want to show that if we were given the odds in em we want to show that the probability is given in it's in deposit. Yeah. Yeah. The odds being in the M. Means the probability of a. To the probability of a compliment is in to end. So the probability of a over the probability of a compliment is in over him. Which tells us the probability of a Over the 1- the probability of ages using complementary is an over him. And so M. P. A. Is equal to n minus N. P. A. When we cross multiply and so am plus and times the probability of a. It is equally in. So the probability of a this in over and plus just like we wanted to show Now and be we were told that the odds of making a sale on a single to call or 2-15 we want to find the probability. So if your odds or 2-15 the newsroom, what we just discussed the probability. Mhm. is to over 17. The 17 just comes from the two past 15. No. And see we're told that the odds of player makes free throws 3-5. Uh And so if the odds 3 to 5, the probability he makes it, there's 38

All right, So where's my car? Sir, we are given the statistics or 29 teams and the 2004 season for the N B. A. Not that any of that information really matters and were given that the probability of scoring two points by making a field goal was point for four, which I'm gonna write down as the probability of F G for field goal and the probability of making a three point shot, which is three p 0.34 All right for part A. We need to find the expected value of shots when you attempt a field goal. And while you earn two points from field goal and the probability of scoring a field goal is 0.44 which checks out to be expected point value 0.88 for part B now wants us find the expected value off a three point shot for these teams. So three point shot makes three points, and we multiply that by 0.34 and that ends up being 1.2 Now Park Si asks us to expect more points. Uh, sorry, it's asking us. Why do coaches love some players 2.3 point shots, even though the probability making two points out is greater. If we look at the expected values, the expected value of a two point shot is less than that of a three point shot, which means, on average you'll score more of shots or your score more points with three point shots than you. Well, to point shots. So, yes, that is why some people won't go for three points instead of two points, even if its rescue There you have it.

In question 35 from section 5.1. It also could be questioned 34 in your textbook, depending on which version you have. But it says 25 25 repetitions of your simulation were performed. The simulated number of makes and each set of 10 shots were recorded on the dot plot below Ultimate we're looking for what is the approximate probability that a 47% shooter makes five or more shots in 10 attempts. So, looking at the simulation, we just want to see how many times five shots orm or were accomplished in this dot plot. So there's 25 total dots. Find the number of dots that air five orm or, in this case, there are 12 total dots that air five arm or out of the 25 so 12 possibilities of five or more out of 25 shots. That gives us C as her answer, which is 12 25


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