Probability

# When a coin is tossed three times what is the probability of getting at most two heads?

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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.

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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 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

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 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 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

Each toss has a 1/2 probability of getting heads. Each toss is an independent event. So three heads in a row (heads AND heads AND heads) would have a probability of:1/2 * 1/2 * 1/2 = (1/2)^3 = 1/(2^3) = 1/8 = 12.5%

the probability of getting one head and one tail on three flips of a coin is 1/9

For 3 coin flips: 87% chance of getting heads at least once 25% chance of getting heads twice 13% chance of getting heads all three times

the probability of getting heads-heads-heads if you toss a coin three times is 1 out of 9.

The probability of getting all heads if you flip a coin three times is: P(HHH) = 1/2 &#8729; 1/2 &#8729; 1/2 = 1/8. The probability of getting all tails if you flip a coin three times is: P(TTT) = 1/2 &#8729; 1/2 &#8729; 1/2 = 1/8. The probability of getting all heads or all tails if you flip a coin three times is: P(HHH or TTT) = P(HHH) + P(TTT) = 2/8 = 1/4.

In a large enough number of tosses, it is a certainty (probability = 1). In only the first three tosses, it is (0.5)3 = 0.125

Each coin toss is a Bernoulli trial with a probability of success of .5. The probability of tossing heads exactly 3 times out of five is3 ~ Bin(5, 1/2), which equals(5!/(3!(5-3)!))(0.5^3)(1-0.5)^(5-3), which is 0.3125.

This is a problem concerning binomial probability distribution. If you have three coins, each one can land heads or tails. (We will ignore the remote chance that a coin will land on its edge.) Each coin has an equal probability of landing heads or tails. In other words, each coin has two possible states. Since there are three coins, there are 2 x 3 = 6 possible states. We can easily see what they are with a table: HHH HHT HTH HTT THH THT TTH TTT Three of those possible eight states contain two and only two heads. So the probability of throwing any of those three states is three in eight, or 3/8 = 0.375.

Ideally, the probability of getting any specific combination of length n is 0.5n = 1/2n. For n = 3, this is 0.125 = 1/8.

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 of something NOT happening is the complement of the probability of something happening. Since the probability that you DO have 3 heads is 1/8 (that is, 1/2 cubed), the complement is 1 - 1/8 = 7/8.

The probability of the first coin landing heads is half (or 1/2). Similarly, the probability of the second and third coins landing heads are also 1/2 in each case. Therefore, the probability of having three heads is: (1/2)(1/2)(1/2) = (1/8)

With 4 coins you have 24 (16) possibilities. If we wanted a specific coin to land 'tails' while the others landed 'heads' we would have one possibilty out of 16. Since we don't care which of the coins lands 'tails,' we have four chances in 16 or a 25 percent chance.

###### ProbabilityMath and ArithmeticStatistics

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