Probability

What is the probability of getting at least 2 heads in three flips of a fair coin?

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In three flips of a fair coin, there are a total of 8 possible outcomes: T, T, T; T, T, H; T, H, T; T, H, H; H, H, H; H, H, T; H, T, H; H, T, T Of the possible outcomes, four of them (half) contain at least two heads, as can be seen by inspection. Note: In flipping a coin, there are two possible outcomes at each flipping event. The number of possible outcomes expands as a function of the number of times the coin is flipped. One flip, two possible outcomes. Two flips, four possible outcomes. Three flips, eight possible outcomes. Four flips, sixteen possible outcomes. It appears that the number of possible outcomes is a power of the number of possible outcomes, which is two. 21 = 2, 22 = 4, 23 = 8, 24 = 16, .... Looks like a pattern developing there. Welcome to this variant of permutations.

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If it is a fair coin, the probability of getting at least one Head from 3 flips is 7/8If it is a fair coin, the probability of getting at least one Head from 3 flips is 7/8If it is a fair coin, the probability of getting at least one Head from 3 flips is 7/8If it is a fair coin, the probability of getting at least one Head from 3 flips is 7/8

As the question is "what is the probability of getting at least one head" the correct way to answer this is to ask what is the probability of not getting any heads and then subtract this from 1.The probability of not getting a head in 4 flips = 0.54 (i.e. 0.5 * 0.5 * 0.5 * 0.5) = 1/16.Therefore the probability of getting at least one head is 1 - 1/16 = 15/16.

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

If you know that two of the four are already heads, then all you need to find isthe probability of exactly one heads in the last two flips.Number of possible outcomes of one flip of one coin = 2Number of possible outcomes in two flips = 4Number of the four outcomes that include a single heads = 2.Probability of a single heads in the last two flips = 2/4 = 50%.

The probability of obtaining 7 heads in eight flips of a coin is:P(7H) = 8(1/2)8 = 0.03125 = 3.1%

Pr(3 flips at least one H) = 1 - Pr(3 flips, NO heads) = 1 - Pr(3 flips, TTT) = 1 - (1/2)3 = 1 - 1/8 = 7/8

The requirement that one coin is a head is superfluous and does not matter. The simplified question is "what is the probability of obtaining exactly six heads in seven flips of a coin?"... There are 128 permutations (27) of seven coins, or seven flips of one coin. Of these, there are seven permutations where there are exactly six heads, i.e. where there is only one tail. The probability, then, of tossing six heads in seven coin tosses is 7 in 128, or 0.0546875.

The probability of getting at least 1 tails is (1 - probability of getting all heads) The probability of getting all heads (no tails) is &frac12; x &frac12; x &frac12; x &frac12; x &frac12; x &frac12; x &frac12; x &frac12; = 1/256 = 0.00390625 so the probability of getting at least ONE tails is 1-0.30390625 = 0.99609375 = 255/256

The probability of obtaining exactly two heads in three flips of a coin is 0.5x0.5x0.5 (for the probabilities) x3 (for the number of ways it could happen). This is 0.375. However, we are told that at least one is a head, so the probability that we got 3 tails was impossible. This probability is 0.53 or 0.125. To deduct this we need to divide the probability we have by 1-0.125 0.375/(1-0.125) = approximately 0.4286

We can simplify the question by putting it this way: what is the probability that exactly one out of two coin flips is a head? Our options are HH, HT, TH, TT. Two of these four have exactly one head. So 2/4=.5 is the answer.

The probability of getting at least one tail in a flip of six coins is the same as the probability of not getting all heads, which is 1 - (0.56), or 0.984375.

With two flips of a coin you can get two heads, two tails, a head and a tail, or a tail and a head. There are a total of four different possible outcomes, and three of them have at least one head. That's 3 out of 4, or 3/4ths. It's also 0.75 which is the probability of getting at least one head with two flips of a coin. Note that as we use the term probability here, it is zero (no chance it can happen at all), or one (it must happen), or something in between. A probability appears in the form of a fraction or decimal, and has no units attached to it.

Probability of no heads = (0.5)^5 = 0.03125Probability of at least one head = 1 - probability of no heads = 1 - 0.03125 = 0.96875

The probability that you will toss five heads in six coin tosses given that at least one is a head is the same as the probability of tossing four heads in five coin tosses1. There are 32 permutations of five coins. Five of them have four heads2. This is a probability of 5 in 32, or 0.15625. ----------------------------------------------------------------------------------- 1Simplify the problem. It asked about five heads but said that at least one was a head. That is redundant, and can be ignored. 2This problem was solved by simple inspection. If there are four heads in five coins, this means that there is one tail in five coins. That fact simplifies the calculation to five permutations exactly.

The probability of tossing a coin 9 times and getting at least one tail is: P(9 times, at least 1 tail) = 1 - P(9 heads) = 1 - (0.50)9 = 0.9980... &asymp; 99.8%

you toss 3 coins what is the probability that you get exactly 2 heads given that you get at least one head?

>>> 1:7 (or, if you like probability, 87.5%)I disagree. There are four possible combinations of three tosses (where order does not matter):HHHHHTHTTTTTThree of these combinations will show at least one head - only by throwing three tails will you not throw at least one head.Thus, the probability of throwing at least one head in three flips is 75%.

The probability of tossing 6 heads in 6 dice is 1 in 26, or 1 in 64, or 0.015625. THe probability of doing that at least once in six trials, then, is 6 in 26, or 6 in 64, or 3 in 32, or 0.09375.

Pr(3H given &gt;= 2H) = Pr(3H and &gt;= 2H)/Pr(&gt;=2H) = Pr(3H)/Pr(&gt;=2H) = (1/4)/(11/16) = 4/11.

Your question is a bit difficult to understand. I will rephrase it as follows: What is the probability of getting a head if a coin is flipped once? p = 0.5 What is the probability of getting 2 heads if a coin is flipped twice = The possible events are HT, TH, HH, TT amd all are equally likely. So the probability of HH is 0.25. What is the probability of getting at least on head if the coin is flipped twice. Of the possible events listed above, HT, TH and HH would satisfy the condition of one or more heads, so the probability is 3 x 0.25 = 0.75 or 3/4. Also, since the probability of TT is 0.25, and the probability of all events must sum to 1, then we calculate the probability of one or more heads to be 1-0.25 = 0.75

Prob(at least 4 heads) = Prob(4 heads) + Prob(5 heads) = 5/32 + 1/32 = 6/32 = 3/16

There are 23 or 8 possible outcomes listed below (H=Head, T=Tails). HHH HHT HTH HTT THH THT TTH TTT each has a 1/8 probability. Count the number that has at least 2 heads and it is 3. So, the probability is 3/8.

50-50. each toss is independent of any previous toss. if all tosses are to be heads/tails then each toss you multiply by the number of chances. i,e. 2, starting with 1. three heads in a row is 1x2x2

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