Quinela In a horse race, a quinela bet is won if you selected ...

Question

Quinela In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 144th running of the Kentucky Derby had a field of 20 horses. What is the probability of winning a quinela bet if you randomly select the horses?

Accepted Answer

Welcome back, everyone. In the soccer tournament, 16 teams have reached the knockout stage. A fan predicts the two teams that will reach the final match in any order, what is the probability that the fans random prediction is correct? A 1 divided by 16, B 1 divided by 120, C 1 divided by 240. In the one divided by 256. So we want to identify the probability of an event A. Let's suppose that A represents that the prediction is correct, and we have to recall that this is the ratio between two numbers, M and N. So let's begin with N, which is the total number of outcomes. We want to choose two teams out of 16, and the order doesn't matter, so we're going to choose combinations. We want to recall that the number of combinations. Is represented by N choose K. In this context, Our Total number of teams is 16, so that's how N and K is 2 we're choosing two teams. So we want to evaluate 16, choose 2. That would be the total number of possible pairs, right? Meaning we can introduce our denominator as 16 choose 2, and for the numerator there is only one pair that is going to be a winning pair, right? Essentially we're going to include 1. And now we want to calculate the result. When we divide 1 by 16, choose 2, we can either use a calculator or separately evaluate 16 choose 2, which is simply. 16 factorial, we take our N factorial divide that by. K factorial, which is two factorial, and also multiply in the denominator by the difference between and and K factorial. 16 minus 2 Victoria. So this gives the 16 factorial divided by 2 factorial, multiplied by 14 factorial. Therefore, The probability is going to be 1 divided by 16 factorial, divided by 2 factorial multiplied by 14 factorial, or basically 2 factorial multiplied by 14 factorial, divided by 16 factorial, and that is going to be 1 divided by 120. Essentially We get this result from the fact that. We get 2 multiplied by 1 from 2 factorial. From 14 factorial, we can just leave it as it is, and now constraining the denominator, 16 factorial is simply 16 multiplied by 15, multiplied by. 14 factorial, right? And this allows us to cancel out 14 factorial. And therefore we get 2 in the numerator, and the denominator we get 16 multiplied by 15. Or basically 1 divided by 8 multiplied by 15, right, because we can divide the numerator and the denominator by 2, and that's 1 divided by 120, which corresponds to the answer choice B. Thank you for watching.

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