Math and Arithmetic
Statistics
Probability

# What is the probability that three coins flipped at the same time will land all 3 heads up?

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###### 2011-05-19 01:43:01

One in eight, or 12.5%.

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## Related Questions

The probability of flipping three heads when flipping three coins is 1 in 8, or 0.125. It does not matter if the coins are flipped sequentially or simultaneously, because they are independent events.

The probability of flipping three tails with three coins is (1 in 2)3 or 1 in 8 or 0.125.

Number of possible outcomes with 4 coins = 2 x 2 x 2 x 2 = 16.Number of successes = 2. (Three heads or four heads)Probaility of success = 2/16 = 1/8 = 12.5 percent

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)

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.

There are 8 permutations of three coins. Of these, 3 of them have two heads, so the probability of tossing two heads on three coins is 3 in 8, or 0.375. However, you said, "at least", so that includes the case of three heads, so the probability of throwing at least two heads is 4 in 8, or 0.5. T T T T T H T H T T H H * H T T H T H * H H T * H H H *

Possibilities: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. There are 3 chances out of 8 that there will be two heads and one more that there will be AT LEAST two heads.

The correct answer is 1/2. The first two flips do not affect the likelihood that the third flip will be heads (that is, the coin has no "memory" of the previous flips). If you flipped it 100 times and it came up heads each time, the probability of heads on the 101st try would still be 1/2. (Although, if you flipped it 100 times and it came up heads all 100 times - the odds of which are 2^100, or roughly 1 in 1,267,650,000,000,000,000,000,000,000,000 - you should begin to wonder about whether it's a fair coin!). If you were instead asking "What is the probability of flipping a coin three times and having it land on "heads" all three times, then the answer is 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.

Because you are thinking permutations rather than combinations. There are four permutations of two coins, but there are only three combinations, because it does not matter which coin is heads and which coin is tails. As a result, the combination of heads and tails has a 0.5 probability, while two heads or two tails each have a 0.25 probability.

There are four outcomes possible (not considering order)HHHHHTHTTTTTOnly in two of the cases are there two or more headsThe probability is 0.5

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 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

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.

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%

If you mean 'at least' 2 heads, the probability is 50%. If you mean exactly 2, the probability is 3/8, or 37.5%. There are 3 independent coin tosses, each of which is equally likely to come up heads or tails. That's a total of 2 * 2 * 2 or 8 possible outcomes (HHH, HHT, HTH, etc.). Of these, 4 include 2 or 3 heads, which is half of 8. Only 3 include exactly 2 heads, so the probability of that is 3/8.

Since each event is independent (heads in one coin does not affect the probability of the other two coin flips), the multiplication rule applies: 1/2 x 1/2 x 1/2 = 1/8 or 0.125. So we can say the probability is 12.5%.

The probability of flipping one coin and getting tails is 1/2. In order to find the probability of multiple events occurring, you find the product of all the events. For 3 coins the probability of getting tails 3 times is 1/8 because .5 x .5 x .5 = .125 or 1/8.

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

The greater the number of coins used, the closer your experimental probability will be to the true value. However, you may never ever get the precise probability - even if you toss a trillion coins!

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