Can some solve for me step by step with explanation on how t

Can some solve for me step by step with explanation on how to get the answer. I am very weak in statistics and have no background. Deeply appreciated. Thanks

1. In the game of Heads or Tails, Betty and Bob toss a coin four times. Betty wins a dollar from Bob for each head and pays Bob a dollar for each tail - that is, she wins or oses the difference between the number of heads and the number of tails. For example, if there are one head and 3 tails, Betty loses $2. You can check that Betty\'s possible outcomes are (-4,-2,0,2,4). Assign probabilities to these outcomes by playing the game 20 times and using the proportions of the outcomes as estimates of the probability. If possible, combine your trials with those of other students to obtain long-run proportions that are closer to the probabilities. (M&M; 4.7)

Solution

Following is the outcome of 20 games:

Following table shows the corresponding probabilties:

Game Number	Head	Tail	Bet Amount (Head-Tail) ($)
1	2	2	0
2	2	2	0
3	1	3	-2
4	1	3	-2
5	1	3	-2
6	0	4	-4
7	1	3	-2
8	4	0	4
9	3	1	2
10	2	2	0
11	1	3	-2
12	1	3	-2
13	3	1	2
14	2	2	0
15	0	4	-4
16	4	0	4
17	1	3	-2
18	2	2	0
19	2	2	0
20	4	0	4