Show transcribed image text As we reported at the beginning of this chapter, on

Question

Show transcribed image text As we reported at the beginning of this chapter, on June 16, 1989, during the second round of the 1989 u.S. Open, four golfers- Doug Weaver, Mark Wiebe, Jerry Pate, and Nick Price-made holes in one on the sixth hole at Oak Hill in Pittsford, New York. Now that you have studied the material in this chapter, you can determine for yourself the likelihood of such an event. According to perts, the odds against a professional golfer making a hole in one are 3708 to 1, in other words, the probability is that a professional golfer will make a hole in one. One hundred fifty-five golfers participated in the second round. Determine the probability that at least 4 of the 155 golfers would get a hole in one on the sixth you make in solving part (a)? Do those assumptions seem reasonable to you? Explain your answer. hole. Discuss your result. What assumptions did

Explanation / Answer

Let the event of getting a hole in one on the sixth hole be denoted by A.

Odds againts the event A = 3708 : 1

So,

P(A) = 1/(3708+1) = 0.00027

So this is a Binomial distribution with the following parameters:

n = 150, p = 0.00027

Let X denote the number of golfers getting a hole in one on the sixth hole.

So, we are asked to calculate P(X >= 4).

Using the formula:

P(X >= 4) = 1 - P(X < 4)

P(X < 4) = P(X=0) + P(X=1) +P(X=2) + P(X=3)

Now,

P(X=0) = nC0*(p^0)*((1-p)^(n-0)) = 150C0*(0.00027^0)*((1-0.00027)^(150-0)) = 0.96

Similarly,

P(X=1) = 150C1*(0.00027^1)*((1-0.00027)^(150-1)) = 0.0389

P(X=2)  = 150C2*(0.00027^2)*((1-0.00027)^(150-2)) = 0.00078

P(X=3)  = 150C3*(0.00027^3)*((1-0.00027)^(150-3)) = 0.00001

So,

P(X < 4) = 0.96 + 0.0389 + 0.00078 + 0.00001 = 0.9997

So,

P(X >= 4) = 1-0.9997 = 0.0003

In calculating the above probability we assumed that the chances of a golfer getting a hole in one on sixth hole is independent of other golfers, which is a reasonable assumption to make since all golfers play individually.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.