Because there are only 2 outcomes for the flip of a coin, for 5 flips you just need to take (1/2)5, which equals 1/32.
This implies there are 32 different outcomes for the case of tossing a coin 5 times. From these 32 outcomes 5 have exactly 4 heads: THHHH, HTHHH, HHTHH, HHHTH, and HHHHT. So the probability of getting exactly 4 heads when you toss a coin 5 times is:
P(4H,!T) = 5/32 = 0.15625 ≈ 15.6%
The probability of getting 3 or more heads in a row, one or more times is 520/1024 = 0.508 Of these, the probability of getting exactly 3 heads in a row, exactly once is 244/1024 = 0.238
About a 1 in 16 chance of getting a coin to land on heads 4 times in a row.
3 out of 8
2/10 --> 1/5
The opposite of getting at most two heads is getting three heads. The probability of getting three heads is (1/2)^2, which is 1/8. The probability of getting at most two heads is then 1 - 1/8 which is 7/8.
The probability of getting 3 or more heads in a row, one or more times is 520/1024 = 0.508 Of these, the probability of getting exactly 3 heads in a row, exactly once is 244/1024 = 0.238
About a 1 in 16 chance of getting a coin to land on heads 4 times in a row.
3 out of 8
2/10 --> 1/5
Since a coin has two sides and it was tossed 5 times, there are 32 possible combinations of results. The probability of getting heads three times in 5 tries is 10/32. This is 5/16.
The probability of flipping a coin 3 times and getting 3 heads is 1/2
The opposite of getting at most two heads is getting three heads. The probability of getting three heads is (1/2)^2, which is 1/8. The probability of getting at most two heads is then 1 - 1/8 which is 7/8.
The probability to get heads once is 1/2 as the coin is fair The probability to get heads twice is 1/2x1/2 The probability to get heads three times is 1/2x1/2x1/2 The probability to get tails once is 1/2 The probability to get tails 5 times is (1/2)5 So the probability to get 3 heads when the coin is tossed 8 times is (1/2)3(1/2)5=(1/2)8 = 1/256 If you read carefully you'll understand that 3 heads and 5 tails has the same probability than any other outcome = 1/256 As the coin is fair, each side has the same probability to appear So the probability to get 3 heads and 5 tails is the same as getting for instance 8 heads or 8 tails or 1 tails and 7 heads, and so on
25%
The probability of getting heads only once when a fair coin is tossed 4 times is 4/16 or 0.25. This is because there are 4 favorable outcomes where heads appears exactly once, out of the 16 possible outcomes.
6.25%
the probability of getting heads-heads-heads if you toss a coin three times is 1 out of 9.