Question

In: Statistics and Probability

Diet Fractions. Roll 2 dice and use the numbers to make a fraction less than or...

Diet Fractions. Roll 2 dice and use the numbers to make a fraction less than or equal to 1. Player A wins if the fraction cannot be reduced; otherwise, player B wins. a. Play the game 50 times and record the results. b. Is the game fair or not? Why or why not? c. Using the sample space for 2 dice, compute the probabilities of winning for player A and for player B. Do these agree with the results obtained in part a?

Solutions

Expert Solution

Hello

(a) Result of playing game 50 times

# First Die Second Die Required Fraction form Reducable?
1 4 6 4/6 Yes
2 2 6 2/6 Yes
3 3 2 2/3 No
4 1 4 1/4 No
5 1 5 1/5 No
6 3 1 1/3 No
7 4 6 4/6 Yes
8 6 6 6/6 Yes
9 6 2 2/6 Yes
10 4 1 1/4 No
11 6 4 4/6 Yes
12 4 1 1/4 No
13 4 1 1/4 No
14 5 6 5/6 No
15 2 4 2/4 Yes
16 6 4 4/6 Yes
17 4 2 2/4 Yes
18 3 3 3/3 Yes
19 1 4 1/4 No
20 5 5 5/5 Yes
21 5 6 5/6 No
22 5 6 5/6 No
23 6 2 2/6 Yes
24 5 4 4/5 No
25 6 1 1/6 No
26 1 2 1/2 No
27 6 1 1/6 No
28 6 6 6/6 Yes
29 2 2 2/2 Yes
30 4 2 2/4 Yes
31 5 5 5/5 Yes
32 5 2 2/5 No
33 6 3 3/6 Yes
34 6 3 3/6 Yes
35 6 1 1/6 No
36 4 3 3/4 No
37 6 5 5/6 No
38 5 6 5/6 No
39 3 6 3/6 Yes
40 1 6 1/6 No
41 4 2 2/4 Yes
42 3 2 2/3 No
43 3 1 1/3 No
44 5 3 3/5 No
45 6 3 3/6 Yes
46 5 1 1/5 No
47 3 3 3/3 Yes
48 5 1 1/5 No
49 3 4 3/4 No
50 5 5 5/5 Yes
Total Reducables 23

(b) Using the data above, P(A winning) = 27/50 = 54% and P(B winning) = 23/50 = 46%.

Hence, the game doesn't seems to be fair.

(c) P(B winning) = 2*[P(rolling 2,3,4,6 as the smaller/equal number and 6 as larger) + P(rolling 5 as the smaller/equal number and 5 as larger) + P(rolling 2,4 as the smaller/equal number and 4 as larger) + P(rolling 3 as the smaller/equal number and 3 as larger) + P(rolling 2 as the smaller/equal number and 2 as larger) + P(rolling 1 as the smaller/equal number and 1 as larger)]

and hence, P(A winning) =

No, they don't agree with the result obtained in part (a)

Don't be rigid in thinking these results as this is just an experiment with only 50 trials. The result in part (a) will most definitely converge with result in part (c) when number of trials becomme very large.

I hope this solves your doubt.

Do give a thumbs up if you find this helpful.


Related Solutions

Partial Fractions: Problem 2 Use the method of partial fraction decomposition to write the following rational...
Partial Fractions: Problem 2 Use the method of partial fraction decomposition to write the following rational expression as the sum of simpler rational functions whose denominators are polynomials of degree 1. −20x+20/x^2−x−56=
We will simulate a dice game in which 2 dice are thrown. If the roll is...
We will simulate a dice game in which 2 dice are thrown. If the roll is 7 or 11, you win. If the roll is 2, 3, or 12, you lose If the roll is any other value, it establishes a point. If with a point established, that point is rolled again before a 7, you win. If, with a point established, a 7 is rolled before the point is rolled again you lose. Build your algorithm incrementally. First write...
A diet needs to be created that contains not less than 2146 calories, not more than...
A diet needs to be created that contains not less than 2146 calories, not more than 58 grams of protein, not less than 10 grams of carbohydrates and not less than 13 grams of fat. Also, the diet should haveminimal cost. In addition the diet should include at least 1 Units of fish and at least 1.2 cup of milk. The diet will consist of the six different foods: Bread, Milk, Cheese, Fish, Potato and Yogurt. The following table lists...
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the marginals pmf's for both variables. c) Are X and Y independent?
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the marginals pmf's for both variables. c) Are X and Y independent?
Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on...
Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the maringals pmf's for both variables. c) Are X and Y independent?
1. Decomose the following fraction into partial fractions (3x)/(5x^(2)-x-6)
1. Decomose the following fraction into partial fractions (3x)/(5x^(2)-x-6)
You roll 48 dice all at once. If you add up only the even numbers rolled,...
You roll 48 dice all at once. If you add up only the even numbers rolled, what is the chance that the sum will be 104 or more??
7. Fractions You can express a fraction as a list: [numerator, denominator]. For example 1 2...
7. Fractions You can express a fraction as a list: [numerator, denominator]. For example 1 2 can be expressed as the list [1,2]. (a) Write a function called factionAdd() that takes two fractions as lists and adds them. For example, fraction([1,2], [3,4]) returns [5,4] (b) Write a function fractionMult() that multiplies two fractions that are passed as lists. [HINT: You may use the following function gcd ( x ; y ) to help you calculate the Greatest Common Divisor, which...
You make a carnival game, where the player rolls two fair dice (in a single roll)...
You make a carnival game, where the player rolls two fair dice (in a single roll) and attempts to roll doubles (meaning both dice show the same number). The player puts down a dollar to play the game. If the player loses, they lose their dollar. If the player wins, they win $3 (and do not lose their original dollar). Answer the following (5 pts total). If you are running the game, what is the expected value of how much...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT