# Probability and Simulation Solved Statistics Sample

QUESTION

1. Excel Simulation #1 (20pts)

Choose One • 20 points

Say that every single class in Full Sail’s Masters Degree in Game Design has a 5% failure rate per month in a 13-month program.

These students that fail a single time, will withdraw (drop) from the program the month following their failure; ex. J. Doe fails Month 3, J. Doe withdraws in Month 4.

Given a cohort of 100 that starts the program, about how many are left at the end of the program? Remember that someone can only pass or fail and we are counting only these 100 that start together.

•

35

•

36

•

37

•

38

•

39

•

40

•

41

•

42

•

43

•

44

•

45

•

46

•

47

•

48

•

49

•

50

•

51

•

52

•

53

•

54

•

55

•

56

•

57

•

58

•

59

•

60

•

61

•

62

•

63

•

64

•

65

•

66

•

67

•

68

•

69

•

70

•

71

•

72

•

73

•

74

•

75

2. Excel Simulation #2 (20pts)

Choose One • 20 points

You are going to simulate a game that rolls four (4) twenty-sided dice. If the rolls total to 20 or less, roll two (2)  more twenty-sided dice and add that to the total.

For instance, if the total of my four die rolls is 32, then that is the score of the game. However, if the total is 17, then I roll two more dice and add that to the total. If these two bonus dice total 20, then the score of that game is 37.

Of ten thousand games (10,000), what is the average score? (choose the closest range)

•

11 through 20

•

21 through 30

•

31 through 40

•

41 through 50

•

51 through 60

•

61 through 70

•

71 through 80

•

81 through 90

•

91 through 100

3. Excel Simulation #3 (20pts)

Choose One • 20 points

You are going to play a game where you bet a dollar and get to flip a coin ten (10) times. If you get four (4) heads in a row, you win. If you make the tenth flip without getting four heads in a row, you lose.

Run this game ten thousand times (10,000).

Approximately what is the probability that you will win? (choose the proper range)

•

0% to 5%

•

6% to 10%

•

11% to 15%

•

16% to 20%

•

21% to 25%

•

26% to 30%

•

31% to 35%

•

36% to 40%

•

41% to 45%

•

46% to 50%

•

51% to 55%

•

56% to 60%

•

61% to 65%

•

65% to 70%

•

71% to 75%

•

76% to 80%

•

81% to 85%

•

86% to 90%

•

91% to 95%

•

96% to 100%

4. –

Choose One • 5 points

You have rolled a fair six-sided die three times and the result has been one all three times. On the fourth roll, what is the probability of rolling a one?

•

1/216

•

1/6

•

5/6

•

1/1296

5. –

Choose One • 10 points

I have filled a bag with differently colored ping-pong balls. There are twenty balls in the bag. Twelve are white, six are orange and two are pink. When I draw a ball from the bag, I remove it. What is the probability that my first draw is a white ball and my second is not?

•

0.240

•

0.400

•

0.253

•

0.421

6. –

Choose One • 5 points

I roll two fair six-sided dice. What is the probability that my roll totals 8?

•

8/36

•

6/36

•

5/36

•

3/36

7. –

Choose One • 5 points

There are four ways to win a game of Civilization V: a military victory, a scientific victory, a cultural victory and a diplomatic victory. If 20% of wins are by a cultural victory, 20% of wins are by a scientific victory and 20% are by a diplomatic victory, what percent of wins are military victories?

•

20%.

•

40%.

•

None.

•

8. –

Choose One • 5 points

In Excel, an anchor(\$) allows you to:

•

Easily fill a series such as 1, 2, 3 to the highest number you choose.

•

Hold a cells column and/or row reference in a formula constant.

•

Conditionally format the text in a cell.

•

Refer to data in another worksheet.

•

Deal with someone who likes to snich.

9. –

Choose One • 10 points

If there is a 5% chance that my Heavy will die, a 10% chance that your Medic will die and if these are independent events, what is the probability that we both stay alive?

•

0.05 or 5%

•

0.5 or 50%

•

0.855 or 85.5%

•

0.9 or 90%

1 Sol. Given, the program is a 13-month program and students, who fail a single time, withdraws their name from the program the month following their failure.

Failure rate per month = 5%

No of students at the starting of the program = 100

No of students who failed in the first month = 5% of 100 = 5

But these students will remain in the program for first month. They will withdraw their names in the second month.

So, no of students in the second month = 100 – (5% of 100) = 0.95 * 100

No of students who failed in the second month will be 5% of (0.95 * 100).

And, no of students in the third month = 95 – {5% of (0.95 * 100)} = 0.95 * 0.95 * 100

Similarly, required no of students left at the end of the program would be 0.9512 * 100 = 54.036 (Approx. 54)

The question has been solved in Excel in the similar way using the above concept.

2 Sol. In the given game, four twenty-sided dice are rolled together. So, the output can be any number between 1 and 20 (both included).

If the sum of these four rolls are less than or equal to 20, then two more twenty-side dice will be rolled.

Then, the score of the game will be the sum of all the rolls.

We have written formula RANDBETWEEN(1,20) in the cell A2 to get a random value between 1 and 20. Similarly, we have copied this formula till F2. If the sum of the values from A2 to D2 will be less than or equal to 20, then the values of E2 and F2 will be added to get the total score.

In the cell G2, we have used IF function using the formula =IF(SUM(A2:D2)>20, SUM(A2:D2),SUM(A2:F2)) and this gives the total score of the game.

We have dragged these formulas from A2:G2 to A10001:G10001. In the cell I4, we have taken the average of all the total scores using the formula =AVERAGE(G2:G10001).

The answer i.e. the average score comes out to be between 41 through 50 (Option d).

Whenever we will click anywhere on the sheet Prob 2, the randomly generated values will get changed, but the answer will always be the same as given above.

3 Sol. In the given game, a dollar is bet, and a coin is flipped 10 times. If we get four heads in a row, we will win the game. If we make the tenth flip without getting four heads in a row, we lose.

We have created random values in the cell A2 using the formula =IF(RAND()<0.5,”H”,”T”), where H means “Head” and T means “Tail”. This will give either “H” or “T” value in the cell. Using the similar function, we have created random values for B2:J2. These are the ten flips of the coin. Now, we concatenated all the outcomes in the adjacent cell K2 using the formula =CONCAT(A2:J2). Now, we have used a conditional function under which if four H values come i.e. HHHH in any cell, it will be counted as TRUE, and it has been replaced by 1. Similarly, if the combination of 10 flips does not contain “HHHH”, it will be counted as FALSE, and replaced by 0. The function used for this purpose is =IF(ISNUMBER(SEARCH(“HHHH”,K2))=TRUE,1,0). We then dragged A2:K2 cells to A10001:K10001 to generate ten thousand (10000) values.

Now, the probability of winning the game has been calculated in the cell N3, using the formula =SUM(L2:L10001)/COUNT(L2:L10001). This is based on the formula of finding probability as required no of outcomes divided by total no of outcomes.

The answer comes to be between 21% to 25% (Option e).

Whenever we will click anywhere on the sheet Prob 3, the randomly generated values will get changed, but the answer will always be the same as given above.

4 Sol. Given that a fair six-sided die has been rolled three times and the result has been one all three times.

Rolling a die is an independent event. So, the probability of rolling a one on the fourth roll will be independent of the previous rolls.

Hence, the required probability is 1/6 (Option b).

5 Sol. Given, there are twenty coloured ping-pong balls in the bag, out of which 12 are white, 6 are orange, and 2 are pink.

Probability of drawing a white ball on the first draw = 12/20

Probability of not drawing a white ball on the second draw = (19-11)/19 = 8/19

Hence, the required probability = (12/20) * ((8/19) = 24/95 = 0.2526 (Rounded to 0.253) (Option c)

6 Sol. Given that two fair six-sided dice have been rolled.

Total no of outcomes = 6 * 6 = 36

Possible cases of total rolls being equal to 8 = (2,6), (3,5), (4,4), (5,3), (6,2)

So, favourable no of outcomes = 5

Hence, Required probability = 5/36 (Option c)

7 Sol. There are four ways to win a game of Civilization V – Military victory, Scientific victory, Cultural victory, and Diplomatic victory.

Percentage of wins by cultural victory = 20%

Percentage of wins by scientific victory = 20%

Percentage of wins by diplomatic victory = 20%

Hence, percentage of wins by military victories = 100% – (20% + 20% + 20%) = 100% – 60% = 40% (Option b)

8 Sol. In Excel, an anchor(\$) allows you to (b) Hold a cells column and/or row reference in a formula constant. (Option b)

9 Sol. Given, Probability of Heavy to die, P(Heavy) = 0.05

Probability of Medic to die, P(Medic) = 0.10

Both these events are independent events.

Hence, Probability of both staying alive

= {1 – P(Heavy)} * {1 – P(Medic)} = (1-0.10) * (1-0.05) = 0.9 * 0.95 = 0.855 or 85.5% (Option c).

Looking for best Statistics Assignment Help. Whatsapp us at +16469488918 or chat with our chat representative showing on lower right corner or order from here. You can also take help from our Live Assignment helper for any exam or live assignment related assistance.