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
To calculate the probability of getting at least four heads when flipping a coin six times, we can use the binomial probability formula. The total number of outcomes for six flips is (2^6 = 64). The probabilities for getting exactly four, five, and six heads can be calculated using the binomial formula, and their sum gives the total probability of getting at least four heads. This results in a probability of approximately 0.65625, or 65.625%.
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
To calculate the probability of getting at least four heads when flipping a coin six times, we can use the binomial probability formula. The total number of outcomes for six flips is (2^6 = 64). The probabilities for getting exactly four, five, and six heads can be calculated using the binomial formula, and their sum gives the total probability of getting at least four heads. This results in a probability of approximately 0.65625, or 65.625%.
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%
It is 0.1042
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.