Question

6. Create a probability distribution for a coin flipping game. That is, toss a coin at least 25 times and keep up with the number of heads and the number of tails. (8 points for each part) a. Compile your data into a probability distribution. Be sure to show that your distribution meets the properties for a probability distribution.

RESULTS

Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Res. T H H H T H H H H T H H T H T H T T H T T H H T H

H15/25=3/5

T 10/25=2/5

3/5+2/5=1

How do you create a distribution for this?

Answer 1

Let
probability of head = p
probability of  tail  =  1-p
Here we have
n=	25
p= 3/5 =	0.6
1-p = 2/5 =	0.4
so binomial probability distribution  is given by
x (number of head)	P(x)
0	1.1259E-10
1	4.22212E-09
2	7.59982E-08
3	8.7398E-07
4	7.21033E-06
5	4.54251E-05
6	0.000227126
7	0.000924725
8	0.003120948
9	0.008842685
10	0.021222445
11	0.043409546
12	0.075966705
13	0.113950058
14	0.146507217
15	0.161157939
16	0.151085568
17	0.119979715
18	0.079986477
19	0.044203053
20	0.019891374
21	0.007104062
22	0.001937471
23	0.000379071
24	4.73838E-05
25	2.84303E-06
sum=	1