Math and Arithmetic
Statistics
Probability

# If a coin is tossed 3 times what is the probability of 3 heads?

001 ###### 2011-02-20 17:18:30

There are 8 possible outcomes when a coin is tossed 3 times. Here they are:

8. Tails, Tails, Tails.

There is only one outcome that is heads, heads, heads, so the probability of three heads coming up in three coin tosses is 1 in 8 or 0.125 for that probability.

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## Related Questions  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. If the coin is fair and balanced, like Fox, then the probability is 50%.  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. 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.   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% 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. Coins do not have numbers, there is only the probability of heads or tails. 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.  If you have tossed a fair, balanced coin 100 times and it has landed on HEADS 100 consecutive times, the probability of tossing HEADS on the next toss is 50%. There are two sides on a coin. The odds are 50:100, or 1:2. Half the time the coin SHOULD land on heads. The question is unclear. What do you mean by "almost heads". Please restate the question. The probability is 0.09766%.Each toss has a &frac12; chance to be heads. To combine probabilities use multiply them. So the probability to get two heads out of two tosses is &frac12; * &frac12;, and three heads out of three tosses is &frac12; * &frac12; * &frac12;. So the exact answer is 0.5^10 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? The probability of a heads is 1/2. The expected value of independent events is the number of runs times the probability of the desired result. So: 100*(1/2) = 50 heads The probability of the coin coming up heads each time is 1/8; likewise for 3 tails. The probability of getting 2 heads and 1 tail (in any order) or 2 tails and 1 head, is 3/8. There are lots of other events whose probability can be calculated when a coin is tossed 3 times, but the question doesn't specify what event is to have its probability calculated. 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 only about 75% because very often it is not equal The probability of 3 heads and 3 tails is 0.3125 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 The probability of a fair coin to land head is 1/2. Since for 4 flips it must land heads each time, the probability of 4 heads is 1/2 * 1/2 * 1/2 * 1/2 = 1/16. Every time a coin is tossed there is a 50 / 50 chances of it coming up heads. There is no rule that says tossing it 100 or 6 times will change this.

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