a) Given this information, what is the overall probability of you making a putt between 10-29 feet? (b) Given that a putt between 10-29 feet was made, use Bayes'

Question

Suppose that when playing disc golf, you find that of the putts you throw between 10 and 29 feet, 50% are 10-14 feet, 25% are 15-19 feet, 15% are 20-24 feet, and 10% are between 25-29 feet. You also find that you make 10-14 foot putts 85% of the time, 15-19 foot putts 65% of the time, 20-24 foot putts 30% of the time, and 25-29 foot putts 10% of the time.

(a) Given this information, what is the overall probability of you making a putt between 10-29 feet?

(b) Given that a putt between 10-29 feet was made, use Bayes' Theorem to find the probability that it was between 15-19

Answer 1

Hello Lilly, you have an interesting two part problem. The first part requires the scientist / investigator (ie you) to construct a probability density (or probability mass function) for x where x is the distance of the attempted 'putt' in a range of 10 to 29 feet. where S is proportion of success in an interval and x is an interval of ranges in feet.

Part (a)

n 1 2 3 4

x 10-14 15-19 20-24 25-29

p(x) .5 .25 .15 .1

S_x .85 .65 .30 .1

The overall probability of success for putts in the 10-29 foot range is the expected value of S and is calculated using the standard equation for that

E[s) = ∑_n=1⁴ p(x_n)S_n

part (b)

given the above probability mass function and Bayes Theorem P(B|A) = P(A|B)P(B)/ P(A) and the corollary that P(B|A) = P(A ∩ B) / P(A)

then given that B is a 15-19 foot putt and A is a successful putt, then the probability of B being 15-19 is easy to calculate because the p would be the number of successful putts made in the 15-19 foot range divided by the total number of successful putts made which would be p(x₂) .

These are the methods for finding the answers to the questions. If you need more help in this you can request a session with me at www.wyzant.com/tutors/David4745.

The ask an expert section is not for free homework help. That is why I gave you the explanation of how to get the answer, and did not give answers. Good luck.