Golf Balls
The local golf store sells an “onion bag” tha...

Question

Golf Balls

The local golf store sells an “onion bag” that contains 35 “experienced” golf balls. Suppose that the bag contains 20 Titleists, 8 Maxflis, and 7 Top Flites. Use a tree diagram like the one in Example 5 to answer the following:

a. What is the probability that two randomly selected golf balls are both Titleists?

Accepted Answer

Welcome back, everyone. In this problem, a hardware kit contains 40 bolts, 25 stainless, 10 brass, and 5 aluminum. Two bolts are chosen at random without replacement. What is the probability that both are stainless? Give your answer as a simplified fraction. A says it's 1/5, B 5/13, C 9/13, and D 1/13. Now how can we find the probability that both are stainless? What do we know about probability? Well, recall that the probability of an event, OK, is equal to the number of favorable outcomes. OK. Divided by the number of total outcomes. So for this event, OK, where we find the probability that both bolts are stainless. OK. It's going to be equal to the number of favorable outcomes, that is the probability we choose 2 stainless stainless bolts from 25 or 25 choose 2 divided by the total number of outcomes. That is the probability we choose 2 bolts from 40 or 40 choose 2. Now how can we find both of these combinations? Well, In this case, since 2 bolts are chosen without replacement and we need to calculate the total number of ways to select 2 bolts from the 40 available bolts, we can use our combination formula which says that the combination or the possibility of choose, or sorry, the total number of ways to choose R from N or N choose R equals N factorial divided by R factorial multiplied by N minus R factorial. So we can use this formula in both our cases because now this means then that 25 choose 2. OK Is going to be equal to 25 factorial divided by 2 factorial multiplied by n minus r or 25 minus 2 or 23 factorial. OK, I know when we calculate this here, it simplifies the 25 multiplied by 24 divided by 2 multiplied by 1, which is equal to 300. On the other hand, 40 choose 2 is going to be equal to 40 factorial divided by 2 factorial multiplied by 40 minus 2 or 38 factorial. And now, in this case that's going to be 40 multiplied by 39 divided by 2 multiplied by 1, which equals 780. So now that we have both of those combinations, we can use them in our probability to find out if both bolts are stainless. OK. And when we do that, it's going to be equal to 300 divided by 780, which is equal to 5/13. This is the probability that both bolts selected are stainless. If we look back at our answer choices, that means then that B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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