3 heads from 5 flips

Annotation category:
Chapter 5

 Note:

The number of possible outcomes of each coin flip is 2 (either heads or tails.) So the probability of either a heads or a tails is 1/2.

In Chapter 2 you learned that the number of possible outcomes of several independent events is the product of the number of possible outcomes of each event individually. So the number of combinations that 2 coin flips will give you is: 2 x 2 = 4. In this case we are flipping 5 coins -- so the number of possibilities is: 2 x 2 x 2 x 2 x 2 = 32.

In case you'd like to scrutinize this point, here is the list of all possible combinations:

Coin        1    2    3    4    5
outcome 1   h    h    h    h    h  (5 h)
2   h    h    h    h    t  (4 h)
3   h    h    h    t    h
4   h    h    t    h    h
5   h    t    h    h    h
6   t    h    h    h    h
7   h    h    h    t    t  (3 h)
8   h    h    t    h    t
9   h    t    h    h    t
10   t    h    h    h    t
11   h    h    t    t    h
12   h    t    h    t    h
13   t    h    h    t    h
14   h    t    t    h    h
15   t    h    t    h    h
16   t    t    h    h    h
17   t    t    t    h    h  (2 h)
18   t    t    h    t    h
19   t    h    t    t    h
20   h    t    t    t    h
21   t    t    h    h    t
22   t    h    t    h    t
23   h    t    t    h    t
24   t    h    h    t    t
25   h    t    h    t    t
26   h    h    t    t    t
27   t    t    t    t    h  (1 h)
28   t    t    t    h    t
29   t    t    h    t    t
30   t    h    t    t    t
31   h    t    t    t    t
32   t    t    t    t    t  (0 h)
(Whew!)

As you can count for yourself, there are 10 possible ways to get 3 heads. Thus, the probability of getting 3 heads from 5 coin flips is: 10/32, or 5/16.

 Find this term in: par # ---- 32 36