# Probability Problem?

Out of the possible sequences of heads and tails, how many sequences contain no heads? How many contain exactly 1 head? Exactly 2 heads? Exactly 3 heads? 4 heads?

Favorite Answer

1h – 4 sequences.

2h – 6 sequences.

3h – 4 sequences.

4h – 1 sequence.

(H, H, H, H), (H, H, H, T), (H, H, T, H), (H, H, T, T), …, (T, T, T, T)

(there are 2^4 = 16 possible outcomes. More generally, if you flip a fair coin n times, then the number of all possible outcomes is 2^n).

I usually just list all the possible outcomes.. It’s only 16 anyway ๐

and to get the probability… e.g. the probability of 1-head outcomes is:

1. list of the 1-head outcomes: (H, T, T, T), (T, H, T, T), (T, T, H, T), (T, T, T, H).

2. the probability = Pr(1 head) = 4 / 16 = .25

use the same process to find the probability of the other kind of outcomes. ๐

The sequence with exactly 1 head = 1/2 * 1/2 * 1/2 * 1/2 = 1/16

The sequence with exactly 2 head = 1/2 * 1/2 * 1/2 * 1/2 = 1/16

The sequence with exactly 3 head = 1/2 * 1/2 * 1/2 * 1/2 = 1/16

The sequence with 4 heads = 1/2 * 1/2 * 1/2 * 1/2 = 1/16

0 heads = 1/16 TTTT

1 head = 4/16 HTTT, THTT, TTHT, TTTH

2 heads = 6/16 HHTT, HTHT, HTTH, THHT, THTH, TTHH

3 heads = 4/16 HHHT, HHTH, HTHH, THHH

4 heads = 1/16 HHHH

2 heads: 2/8

3 heads: 3/16

4heads: 0/4

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