Math and Arithmetic

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If you flip a coin 2 times, there are 4 possible outcomes; HH, HT, TH, TT.

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0Four outcomes, three combinations.

Two possible outcomes for each flip. 2,048 possible histories of 11 flips.

I am guessing SamJoe, means SAM and JOE not one person, so three people flip a coin, we have two outcomes each times, so 23= 8 possible outcomes. If you had n people, there would be 2n outcomes. For example, if two people flip there are 4 outcomes HH TT HT or TH

The sample space consists of all the possible outcomes. A flip of a coin has 2 outcomes, H,T. The total number of outcomes for 6 flips are 26 or 64.

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

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).

Two mutually exclusive outcomes. You flip a coin, and only heads and tails are possible.

2. There is heads and there is tails.

If you can identify the outcomes with who flipped each coin: eg Joe and Mary = Heads, Sam = Tails, then 23 = 8. Otherwise, 4.

3 ways, out of 12 possible outcomes.

There are 2 possibilities for each toss. Since the three tosses are independent (one trial does not affect the outcome of the other trials), there are 2 * 2 * 2 = 8 total possible outcomes. The outcomes are: HHH HHT HTH HTT THH THT TTH TTT

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.

If you disregard the sequence of outcomes, there are 6 possible outcomes: 0H 5T 1H 4T 2H 3T 3H 2T 4H 1T and 5H 0T If not, there are 25 = 32 outcomes: TTTTT, TTTTH, TTTHT etc.

as many times as you flip it

Anything is possible!

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

Each flip has two possible outcomes and they are independent events, so there are 24 = 16 possible results. Of these, only 2 (HHHH, TTTT) are the same 4 each time, Thus: probability = 2/16 = 1/8

The probability of a flipped coin landing heads or tails will always be 50% either way, no matter how many times you flip it.

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 ≈ 15.6%

HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT.

Ok, sounds like a trick question. Obviously, there can be only one result, either heads or tails. Generally, when we consider the set of possible outcomes, we would say a coin flip has 2: a head and a tail. If I really want to complicate the matter, I could include that the coin might land on an edge. Don't think its realistic to include landing on an edge as an outcome. Ok, sounds like a trick question. Obviously, there can be only one result, either heads or tails. Generally, when we consider the set of possible outcomes, we would say a coin flip has 2: a head and a tail. If I really want to complicate the matter, I could include that the coin might land on an edge. Don't think its realistic to include landing on an edge as an outcome.

If you roll a standard die and flip a penny at the same time, there are 12 possible outcomes. You can find this out quickly by multiplying the number of outcomes of the coin (2) by the number of outcomes of the die (6). Here they are: Heads, 1 Heads, 2 Heads, 3 Heads, 4 Heads, 5 Heads, 6 Tails, 1 Tails, 2 Tails, 3 Tails, 4 Tails, 5 Tails, 6

The probability of 'heads' on any flip is 50% .

50%. there are only 2 choices heads or tails and that doesn't change no matter how many times you flip the coin

Not really. The theory(that if you have some process that can come out in multiple ways, then, over a long period of tests, the results will be about even if each of the possible outcomes has an equal chance of occurrence isn't literal. If you do flip the coin many more times, then the results will gravitate towards an even amount of occurrences, although it is unlikely for to be split perfectly evenly.

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