The local golf store sells an \"onion bag\" that contains 35 \"experienced\" gol

Question

The local golf store sells an "onion bag" that contains 35 "experienced" golf balls. Suppose the bag contains 20 Titleists, 8 Maxflis, and 7 Top-Flites. What is the probability that you draw (without replacement) a Titleist, and then a Maxflis, and then another Titleist? 1) 2) What is the probability that you draw a Top-Flite or a Maxflis? You attend a 10 horse race and decide to guess what the top 3 finishers of that race will be 3) What is the probability that you pick the first, second, and third place finisher correctly?

Explanation / Answer

1)

Out of 35 balls, 20 are Titleist so

P(Titleist) = 20/35

After that 34 balls are remaining. Out of these 34 balls, 8 are maxflis so

P(maxflis | Titleist) = 8 / 34

After that 33 balls are remaining. Out of these 33 balls, 7 are Top-Flites so

P(Top-Flites | Maxflis and Titleist) = 7 / 33

Now the required probabiltiy is

P(Top-Flites and Maxflis and Titleist) =P(Top-Flites | Maxflis and Titleist)P(Maxflis | Titleist) P(Titleist) =(7/33) * (8/34) *(20/35) = 0.0285

2)

P(Top-Flites or Maxflis) = P(Top-Flites) + P(Maxflis) = 20/35 + 8/35 = 0.80

3)

Number of ways of selecting top 3 finishers is

10*9*8=720

Out of these possible orders, only one is correct so required probability is

P(correct order) = 1/720

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