Question

If you flip a fair coin 7 times, what is the probability of each of the following ?

Answer 1

1/28 chance

Step-by-step explanation:

This means there is a 1 out of 128 chance of getting seven heads on seven coin flips. If we do the math, this is a probability of 0.0078 (rounded to four places).

Answer 2

The probability of getting 7 heads, 0 heads, 1 head, 6 heads, and 2 heads when flipping a fair coin 7 times are 1/128, 1/128, 7/128, 7/128, and 21/128 respectively.

Step-by-step explanation:

In order to find the probability of each event, we need to use the formula:

P(event) = Number of favorable outcomes / Number of possible outcomes

The number of possible outcomes when flipping a fair coin 7 times is 2^7 = 128 (each coin flip has 2 possible outcomes - heads or tails).

1. The number of favorable outcomes for getting 7 heads is 1 (HHHHHHH).
2. The number of favorable outcomes for getting 0 heads is 1 (TTTTTTT).
3. The number of favorable outcomes for getting 1 head is 7 (HTTTTTT, THTTTTT, TTHTTTT, TTTHTTT, TTTTHTT, TTTTTHT, TTTTTTH).
4. The number of favorable outcomes for getting 6 heads is 7 (HHHHHHT, HHHHHTH, HHHHTHH, HHHTHHH, HHTHHHH, HTHHHHH, THHHHHH).
5. The number of favorable outcomes for getting 2 heads is 21 (HHTTTTH, HTHTTTH, HTTHTTH, HTTTHTH, HTTTTHH, THHTTTH, THTHTTH, THTTHTH, THTTTHH, TTHHTTH, TTHHTHH, TTHTTHH, TTTHTHH, HHHTTTH, HHTHTTH, HHTTHTH, HHTTTHH, HTHHTTH, HTHTHTH, HTHTTHH, HTTHHTH).

Therefore, the probabilities are as follows:

1. P(7 heads) = 1/128
2. P(0 heads) = 1/128
3. P(1 head) = 7/128
4. P(6 heads) = 7/128
5. P(2 heads) = 21/128