Question

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?

Answer 1

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.

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