Question

I have a question, which I cannot find the correct solution to from my book.

- Your school Ping-Pong team is not performing very well this season. After some rough calculations, you found out that your team's probability of winning a game is about 0.45. A fellow team member want to know more and asked you also to determine the following.
a) The probability of the team winning 2 games out of 5

b) The probability of winning 10 times out of 25

Thank you so much in advance! I have answered the question myself, but would like to compare to someone else's answer to be sure that I am thinking correctly.
All the best,
Naomi

Answer 1

p = 0.45, q = 1 - p = 0.55

The binomial probability formula is P(x) = C(n, x) p^x q^(n - x)

(a) n = 5, x = 2

x	P(x) = C(5, x) 0.45^x 0.55^(5 - x)
0	0.0503
1	0.2059
2	0.3369
3	0.2757
4	0.1128
5	0.0185

P(2) = 0.3369

(b) n = 25, x = 10

x	P(x) = C(25, x) 0.45^x 0.55^(25 - x)
0	0.0000
1	0.0000
2	0.0001
3	0.0004
4	0.0018
5	0.0063
6	0.0172
7	0.0381
8	0.0701
9	0.1084
10	0.1419
11	0.1583
12	0.1511
13	0.1236
14	0.0867
15	0.0520
16	0.0266
17	0.0115
18	0.0042
19	0.0013
20	0.0003
21	0.0001
22	0.0000
23	0.0000
24	0.0000
25	0.0000

P(10) = 0.1419