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How many possible outcomes of tossing a coin 10 times have at least 2 heads?
Wiki User
∙ 13y ago
There are 210 total possible outcomes from flipping a coin 10 times.
There is one possible outcome where there are 0 heads.
There are 10 possible outcomes where there is 1 head.
So there are 210 - 11 possible outcomes with at least 2 heads.
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Wiki User
∙ 13y ago
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What is the probability of tossing a coin 9 times and getting at least one tail?
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... ≈ 99.8%
What is the probability of getting 2 heads when you toss three coins?
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.
If you flip a coin 8 times how many possible outcomes are there?
The following notes answer the above question completely and neatly. It's better in maths to try to keep it simple.Looking at the different possible outcomes; let H = Head and T = Tail. Then the different possible outcomes are (8H +0T) meaning 8 Heads and Zero Tails, or (7H + 1T) or (6H + 2T) or (5H + 3T) or (4H + 4T) or (3H + 5T) or (2H + 6T) or (1H + 7T) or (0H + 8T) giving 9 different outcomes (possibilities).The 9 different outcomes are not equally probable, (8H + 0T) and (0H + 8T) are the least likely while (4H + 4T) will be the most likely. However, totaling all possible outcomes there are 256.----------------------------------------------------------------------------------------------There are 256 possible "histories" of the whole session, corresponding tothe number of possible values of one binary 'byte', where each flip fills inone bit of the byte.----------------------------------------------------------------------------------------------Another Answer:As is usual in science, the answer depends on how you look at the problem, and on your definition of the terminology that you use. Nine different outcomes, as described above, is correct when you decide to consider only distinguishable or, more, correctly, combinatorial, outcomes.However, in statistics and probability, we don't usually deal with combinations, we deal with permutations, because looking at permutations allows you to see the indistinguishable outcomes, outcomes which do, in fact, affect the probability of the result.In this case, throwing a coin 8 times (or with identical results, throwing 8 coins one time), there are multiple permutations that yield the same combination. For instance, there are eight permutations of one coin being heads, there are 28 permutations of two coins being heads, and so on and so forth, leading up to a grand total of 256 different permutations of 8 coins, yielding "only 9 outcomes".So, in summary, there are 9 distinguishable "outcomes", or combinations, while there are 256 indistinguishable "outcomes", or permutations.(To clarify "indistinguishable", I should say that you could certainly mark each coin with a number, say from 1 to 8, and then you would be able to distinguish the outcomes or heads or tails as a function of which coin was thrown. Similarly, throwing only one coin at a time, you could write down the outcomes as they occur, and they would certainly be "distinguishable". In this context, "indistinguishable" simply means that, in the absence of some tracking system, a throw, for instance, of HTTTTTTT, or THTTTTTT, would not be different - they would both be counted as (1H + 7T), using the notation of the earlier answer.)Now, to nail this down for completeness sake, because the answer does matter, even though the question did not ask it, take a look at probability...Probability is simply the number of permutations of a desired result divided by the number of permutations of all results. Since there is one permutation of no heads (0H + 8T), the probability of no heads is 1 in 256, or about 0.00391. On the other hand, since there are 8 permutations of one head (1H + 7T), the probability of one head is 8 in 256, or about 0.0313. Going one more step, the probability of two heads is 28 in 256, or about 0.109.Understanding the distinction between combinations and permutations, and distinguishable versus indistinguishable, is key to understanding probability.
What is the probability of getting a tail if a coin is tossed twice?
75%. There are 3 possible ways of getting at least one tail from 2 tosses from a coin:Tail & Tail orHead & Tail orTail & HeadEach of these individual outcomes has a probability of 25% (e.g. the probability of getting a tail and then another tail is 25%). Adding the possible outcomes together gives you a total of 75%.
Fair coin is tossed 11 times What is the probability that a Exactly 9 heads appear b At least two heads appear c At most 8 heads appear?
Prob(Exactly 9 Heads) = 0.0269 Prob(At least 2 Heads) = 0.0327 Prob(At most 8 Heads) = 0.9673
What is the probability to get tail at least once when 6 coins are tossed simultaneously?
Number of possible outcomes of one coin = 2Number of possible outcomes of six coins = 2 x 2 x 2 x 2 x 2 x 2 = 64Number of possible outcomes with six heads = 1Probability of six heads = 1/64Probability of not six heads = at least one tails = 63/64 = 98.4375%
What is the probability of tossing a coin 5 times and getting at least one tail?
There are 2^5 (2*2*2*2*2), or 32, possible outcomes of tossing a coin 5 times. Only one of those outcomes does not contain any tails. This leaves us with 31/32, or 97% chance of at least one toss coming up tails.
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 is the probability of of tossing heads on the first 6 tosses of a fair coin?
The probability of tossing heads on all of the first six tosses of a fair coin is 0.56, or 0.015625. The probability of tossing heads on at least one of the first six tosses of a fair coin is 1 - 0.56, or 0.984375.
What is the probability of tossing at least three heads if a fair coin is tossed four times?
It is 0.3125
What is the probability of getting at least 2 heads in three flips of a fair coin?
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.
What is the probability of tossing a coin 6 times and obtaining at least 3 consecutive heads?
The probability is 5/16.
Getting at least one head when tossing eight fair coins?
Is possible.
Probability of getting 1 head tossing two coins?
By tossing two coins the possible outcomes are:H & HH & TT & HT & TThus the probability of getting exactly 1 head is 2 out 4 or 50%. If the question was what is the probability of getting at least 1 head then the probability is 3 out of 4 or 75%
When tossing 5 coins simultaneously what is the probability that at least 1 head is showing?
Probability of no heads = (0.5)^5 = 0.03125Probability of at least one head = 1 - probability of no heads = 1 - 0.03125 = 0.96875
What is the probability of tossing a coin 9 times and getting at least one tail?
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... ≈ 99.8%
Three coins are flip at the same time What is the probability that the outcome is at least 2 heads?
There are four outcomes possible (not considering order)HHHHHTHTTTTTOnly in two of the cases are there two or more headsThe probability is 0.5
