Suppose a miniature golf player sinks a hole-in-one once for every game (10 holes) out of 18 attempts at the game.

part a: design a simulation.

design and conduct a simulation to estimate the likelihood that the golfer will sink at least two holes-in-one during a single game. be sure to show all work for the five steps of simulation.

part b: apply your findings.

using your findings from part a, answer the following questions:

what is the probability the golfer got zero or one hole-in-one during a single game?
what is the probability the golfer got exactly two holes-in-one during a single game?
what is the probability the golfer got six holes-in-one during a single game?

part c: compare.

according to puttputt. net, in 2016 the average mini golfer had a 24% chance of sinking two or more holes-in-one per game.

compare this probability with your conclusion in part a.
what do you think contributed to the probabilities being so different?

Step-by-step explanation:

Project Option 1: Fore!

Suppose a miniature golf player sinks a hole-in-one about 12% of the time on any given hole and is going to play 8 games at 18 holes each.

Part A: Design a simulation.

Design and conduct a simulation to estimate the likelihood that the golfer will sink at least two holes-in-one during a single game. Be sure to show all work for the five steps of simulation.

What is the probability that a golfer hits a certain number of holes-in one in an 18 hole golf game?

The probability of hitting a hole in one per hole is 12%. Each hole is independent of the other.

A random number generator is used to find digits between 00-99. For every digit between 88-99 that appears, it is the same as hitting a hole-in-one.  

Simulated Numbers:

56

96

32

25

16

10

74

45

27

98

56

50

20

31

59

24

47

19

21

49

97

99

98

48

34

39

58

55

18

99

81

03

80

53

44

41

46

64

91

54

34

04

21

00

45

65

46

27

85

44

32

11

48

34

12

74

00

87

92

55

66

94

98

18

58

38

92

90

99

90

74

76

21

14

23

75

70

64

83

89

19

97

74

25

19

96

32

29

35

77

18

36

08

23

81

46

36

77

13

86

34

97

68

75

57

66

74

30

44

43

45

36

69

15

90

37

02

41

01

70

52

28

87

29

57

23

06

07

84

77

78

26

05

77

97

64

01

12

41

09

48

89

93

13

Based on the simulation the probability that the golfer hits at least one hole-in-one in a game is very high at 87.5%. The probability that the golfer gets 3 or more holes-in-one is also reasonably high at 50%.

Part B: Apply your findings.

Using your findings from part A, answer the following questions:

What is the probability the golfer got zero or one hole-in-one during a single game?

In the simulated golf games, the golfer hit one or fewer hole-in-ones ⅜ or 37.5% of the time.

What is the probability the golfer got exactly two holes-in-one during a single game?

The golfer had only one out of eight games with exactly 2 holes-in-one or 12.5% of the time.

What is the probability the golfer got six holes-in-one during a single game?

The golfer never got 6 holes-in-one in the simulation, so in this case 0.

Part C: Compare.

According to PuttPutt.net, in 2016 the average mini golfer had a 24% chance of sinking two or more holes-in-one per game.

Compare this probability with your conclusion in part A.

In this simulation, the mini-golfer had a ⅝ or 62.5% chance of sinking two or more holes-in-one per game. This would mean that the simulated mini-golfer has a significantly higher chance of sinking 2 or more holes-in-one.

What do you think contributed to the probabilities being so different?

The golfer in question might be better than PuttPutt.net's average golfer and the simulation may have just happened to unnaturally favor a better result for the mini-golfer.

a: 1/6, j: 1/4

step-by-step explanation: you are welcome