Math and Arithmetic
Statistics

# How many possible outcomes of tossing one coin 3 times have exactly 2 heads?

567

###### 2012-04-06 04:12:24

3 - hht, hth, thh

I TRIED to use capital letters and got a "take the caps lock off".

I have always used capital letters to indicate heads and tails, but the answer is 3.

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## Related Questions

The outcomes are: heads, tails, tails or tails, heads, tails or tails, tails, heads. You can see that there are 3 possible outcomes with exactly 1 head.

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.(1013)

Heads or tails; each have a probability of 0.5 (assuming a fair coin).

There are 4 possible outcomes, HH, HT, TH, TT. If we assume the odds of tossing heads or tails on any toss is 1/2 (50:50) the odds of tossing heads twice in a row is 1/4 (or 25%).

Each coin can come out either heads (H) or tales (T). Since you're tossing four coins at once, I'm assuming there is no sense of order to be accounted for. In that case, the possible outcomes are the following: HHHH HHHT HHTT HTTT TTTT

The possible outcomes of a coin that is flipped are heads or tails.

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%.

There are 24 = 16 ordered outcomes, that is outcomes in which the order of the results is relevant. If not, there are 5 outcomes (0 heads, 1 head, 2 heads, 3 heads and 4 heads).

If each coin is a different color, then there are 32 possible outcomes. If you can't tell the difference between the coins, and you're just counting the number of heads and tails, then there are 6 possible outcomes: 5 heads 4 heads 3 heads 2 heads 1 heads all tails

Since each coin would have the outcome with Heads and Tails: Then among the 32 coins, we can have the possible outcomes from no Heads, 1 Head, 2 Heads, ....... , 31 Heads, 32 Heads. Therefore we would have 33 outcomes.

With 3 coin tosses, the possible outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT There are 8 possible outcomes and 3 of them have 2 heads. Thus: probability = 3/8 (= 0.375)

The sample space for rolling a die is [1, 2, 3, 4, 5, 6] and the sample space for tossing a coin is [heads, tails].

252/1024 or 0.246. One method of calculating it is this: The total number of outcomes possible by tossing a coin 10 times is 2 to the 10th, which is 1024. In addition, getting 5 heads in 10 tosses is like arranging 5 identical objects in 10 spaces (the remaining 5 spaces are by default Tails), which can be done in 10C5 ways, which is 252. So the probability of getting 5 heads is 252/1024.

Each leaf of the tree is one outcome. To take a simple example, consider the tree for three flips of a coin. The root splits into heads/tails, then each of the two branches splits into heads/tails, and finally each of the four branches splits into heads/tails, for 8 possible outcomes. In this simple case, each of the outcomes is equally probable. To find how many outcomes have exactly two heads, follow each branch of the tree, and put a star by the leaf each time you count two heads. You will find three leaves with exactly two heads (HHT, HTH, and THH). Add the probabilities of these three leaves, to discover that the probability of exactly three heads is 3/8.

Because there are only 2 outcomes for the flip of a coin, for 5 flips you just need to take (1/2)5, which equals 1/32. This implies there are 32 different outcomes for the case of tossing a coin 5 times. From these 32 outcomes 5 have exactly 4 heads: THHHH, HTHHH, HHTHH, HHHTH, and HHHHT. So the probability of getting exactly 4 heads when you toss a coin 5 times is: P(4H,!T) = 5/32 = 0.15625 &asymp; 15.6%

Tossing two coins doesn't have a probability, but the events or outcomes of tossing two coins is easy to calculate. Calling the outcomes head (H)or tails (T), the set of outcomes is: HH, HT, TH and TT as follows: 2 heads = (1/2) * (1/2) = 1/4 1 head and 1 tail, can be heads on first coin tails on second, or just the opposite, there's two possible events: (1/2)*(1/2) + (1/2)*(1/2) = 1/2 2 tails = same probability as two heads = 1/4

enless you include it landing on it's side the two possible outcomes for this are: Heads and Tails

With 5 coin tosses there are 32 possible outcomes. 10 of these have exactly 2 heads, and 26 of these have 2 or more heads.For exactly two coins are heads: 10/32 = 31.25%For two or more heads: 26/32 = 81.25%

It depends on the definition of an outcome. If you care about the order of the tosses, &lt;br /&gt; you get 2 possible outcomes per toss. Three tosses give you 2*2*2=8 possible outcomes. If you only care about the final number of heads and tails, there are 4 possible outcomes (3 heads, 2 heads and a tail, a head and two tails, or 3 tails).

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