Math and Arithmetic
Statistics
Probability

# What is the probability of obtaining exactly seven heads in eight flips of a coin given that at least one is a head?

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The probability of obtaining 7 heads in eight flips of a coin is:

P(7H) = 8(1/2)8 = 0.03125 = 3.1%

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## Related Questions

### What is the probability of obtaining exactly six heads in seven flips of a coin given that at least one is a head?

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.

### What is the probability of obtaining exactly two heads in three flips of a coin given that at least one is a head?

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

### What is the probability of obtaining exactly four heads in five flips of a coin given that at least three are heads?

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.

### What is the probability of obtaining exactly four tails in five flips?

Assume the coin is fair, so there are equal amount of probabilities for the choices.There are two possible choices for a flip of a fair coin - either a head or a tail. The probability of getting a head is &frac12;. Similarly, the probability of getting a tail is &frac12;.Use Binomial to work out this problem. You should get:(5 choose 4)(&frac12;)4(&frac12;).(5 choose 4) indicates the total number of ways to obtain 4 tails in 5 flips.(&frac12;)4 indicates the probability of obtaining 4 tails.(&frac12;) indicates the probability of obtaining the remaining number of head.Therefore, the probability is 5/32.

### What is the probability of obtaining four tails in five flips of a coin?

Assume the coin is fair, so there are equal amount of probabilities for the choices.There are two possible choices for a flip of a fair coin - either a head or a tail. The probability of getting a head is &Acirc;&frac12;. Similarly, the probability of getting a tail is &Acirc;&frac12;.Use Binomial to work out this problem. You should get:(5 choose 4)(&Acirc;&frac12;)4(&Acirc;&frac12;).(5 choose 4) indicates the total number of ways to obtain 4 tails in 5 flips.(&Acirc;&frac12;)4 indicates the probability of obtaining 4 tails.(&Acirc;&frac12;) indicates the probability of obtaining the remaining number of head.Therefore, the probability is 5/32.

### What is the probability of exactly three heads in four flips of a coin given at least two are heads?

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%.

### What are the odds against getting exactly two heads in three successive flips of a coin?

Three in eight are the odds of getting exactly two heads in three coin flips. There are eight ways the three flips can end up, and you can get two heads and a tail, a head and a tail and a head, or a tail and two heads to get exactly two heads.

### What is the probability of two consecutive different coin flips?

The probability is 1/2 if the coin is flipped only twice. As the number of flips increases, the probability approaches 1.

### What is the probability of flipping a head when you roll a coin 3 times?

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

### When tossing 2 coins the probability of getting exactly 1 tail is one over 3?

No, the possible results of two coin flips are; HH HT TH TT The probability of getting exactly one tail is 1/2 or 50%.

### What is the probability of obtaining exactly three heads in four flips of a coin given that at least two are heads?

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

### What is the probability of obtaining exactly 4 heads in 6 flips of a fair coin?

The probability of a head in one flip is 1/2. The probability of HHHHTT is (1/2)6 = 1/64 The possible correct flips are HHHHTT, HHHTHT, HHTHHT, HTHHHT, THHHHT, HHHTTH, HHTHTH, HTHHTH, THHHTH, HHTTHH, HTHTHH, THHTHH, HTTHHH, THTHHH, TTHHHH, each with a probability of 1/64. Total probability is 15/64.

### What is the probability of obtaining exactly four tails in five flips of a coin given that at least three are tails?

The probability is that the remaining two outcomes are 1 H and 1 T. The probability of that is 2/4 or 50%The probability is that the remaining two outcomes are 1 H and 1 T. The probability of that is 2/4 or 50%The probability is that the remaining two outcomes are 1 H and 1 T. The probability of that is 2/4 or 50%The probability is that the remaining two outcomes are 1 H and 1 T. The probability of that is 2/4 or 50%

### What is the probability of obtaining exactly three heads in four flips of a coin given that at least one is a head?

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

### What is the probability of a coin landing heads up on two consecutive flips?

In an infinite series of flips it is 1 = a certainty.In only two flips it is 1/4.In an infinite series of flips it is 1 = a certainty.In only two flips it is 1/4.In an infinite series of flips it is 1 = a certainty.In only two flips it is 1/4.In an infinite series of flips it is 1 = a certainty.In only two flips it is 1/4.

### Why is it called experimental probability?

It's difficult to think of a real event to which an exact probability can be assigned. We say that flipping a coin yields 'heads' with probability 1/2 but we do not know that definitely. The only way of assigning a probability in the sense of numbers of heads versus total numbers of flips is by experiment. (Be aware though that there are other interpretations of the word probability.) If I were to flip a coin 500 times and obtained 249 heads then the experimental probability of obtaining a head would be 249/500 or 0.498.

### What is the probability of obtaining exactly five heads in six flips of a coin given that at least one is a head?

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.

### What is the probability of obtaining exactly four tails in five flips of a coin if at least three are tails?

We need to determine the separate event. Let A = obtaining four tails in five flips of coin Let B = obtaining at least three tails in five flips of coin Apply Binomial Theorem for this problem, and we have: P(A | B) = P(A &cap; B) / P(B) P(A | B) means the probability of "given event B, or if event B occurs, then event A occurs." P(A &cap; B) means the probability in which both event B and event A occur at a same time. P(B) means the probability of event B occurs. Work out each term... P(B) = (5 choose 3)(&frac12;)&sup3;(&frac12;)&sup2; + (5 choose 4)(&frac12;)4(&frac12;) + (5 choose 5)(&frac12;)5(&frac12;)0 It's obvious that P(A &cap; B) = (5 choose 4)(&frac12;)4(&frac12;) since A &cap; B represents events A and B occurring at the same time, so there must be four tails occurring in five flips of coin. Hence, you should get: P(A | B) = P(A &cap; B) / P(B) = ((5 choose 4)(&frac12;)4(&frac12;))/((5 choose 3)(&frac12;)&sup3;(&frac12;)&sup2; + (5 choose 4)(&frac12;)4(&frac12;) + (5 choose 5)(&frac12;)5(&frac12;)0)

### What is the probability that three coin flips will have at least one head?

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

### Probability to get exactly 2 heads when flipping a coin 3 times?

The probability of throwing exactly 2 heads in three flips of a coin is 3 in 8, or 0.375. There are 8 outcomes of flipping a coin 3 times, HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. Of those outcomes, 3 contain two heads, so the answer is 3 in 8.

### What is the probabity of obtaining three heads?

On a fair 50-50 coin, the chance of you getting heads 3 times in a row is .5 * .5 * .5 which is 12.5% Getting exactly 3 heads out of any number of coin flips involves: (Number of Flips!/ [6 * (N-3)!]) * (.5^3)* (.5^(n-3))