Math and Arithmetic
Statistics
Probability

# What is the probability of getting exactly 3 heads if a fair coin is tossed 8 times?

###### Answered 2011-06-13 00:13:50

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

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## Related Questions

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 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 mathematical probability of getting heads is 0.5. 70 heads out of 100 tosses represents a probability of 0.7 which is 40% larger.

The answer depends on how many times the coin is tossed. The probability is zero if the coin is tossed only once! Making some assumptions and rewording your question as "If I toss a fair coin twice, what is the probability it comes up heads both times" then the probability of it being heads on any given toss is 0.5, and the probability of it being heads on both tosses is 0.5 x 0.5 = 0.25. If you toss it three times and want to know what the probability of it being heads exactly twice is, then the calculation is more complicated, but it comes out to 0.375.

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

There is 24 or 16 outcomes. There is 4 ways to get heads once (HTTT &amp; THTT &amp; TTHT &amp; TTTH). So, the probability of getting heads only once if a fair coin is tossed 4 times is 4/16 or 1/4.

If a fair coin is tossed 5 times, the probability of getting 5 heads is:P(H,H,H,H,H) = (1/2)5 = 1/32 = 0.03125 = 3.125% &acirc;&permil;&circ; 3.1%

With 5 coin tosses there are 32 possible outcomes. 10 of these have exactly 2 heads, and 26 of these have 2 or more heads.For exactly two coins are heads: 10/32 = 31.25%For two or more heads: 26/32 = 81.25%

0.5, 1/2, 50% The probability for heads versus tails does not change based on the amount of times the coin is tossed. It will always be a 50% chance.

There is a 50% chance that it will land on heads each toss. You need to clarify the question: do you mean what is the probability that it will land on heads at least once, exactly once, all five times?

One in four. 1:4. The probability of getting heads when a fair coin is tossed is: P(H) = 1/2. The probability of getting heads on a second toss is: P(H) = 1/2, this result is independent of the result of the first toss. The probability of having both events happen (heads on the first and heads on the second toss) is: P(H1UH2) = (1/2)&#8729;(1/2) = 1/4 = 0.25 = 0.25%

only about 75% because very often it is not equal The probability of 3 heads and 3 tails is 0.3125

The number of times a coin is tossed does not alter the probability of getting heads, which is 50% in every case, as long as the coin has not been rigged (i.e., a double-headed coin, a weighted coin) to alter the result.

Coins do not have numbers, there is only the probability of heads or tails.

The probability of getting 8 heads out of 10 tosses is (10C8)(1/2)^8 (1/2)^2 = 45 / 1024 = 0.0439. It is assumed that the probability of getting a head in a single toss is 1/2. 10C8 = 10 x 9 / 1 x 2 = 45

The probability of getting five heads out of 10 tosses is the same as the probablity of getting five tales out of ten tosses. One. It will happen. When this happens, you will get zero information. In other words, this is the expected result.

The sample space is 23 or 8; which can be listed out as: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. There are 2 of the 8 that have exactly 2 heads; so the probability of exactly two coins landing on heads is 2/8 or 1/4.

The probability that both coins are heads is the probability of one coin landing heads multiplied by the probability of the second coin landing heads: (.5) * (.5) = .25 or (1/2) * (1/2) = 1/4

About a 1 in 16 chance of getting a coin to land on heads 4 times in a row.