how many possible outcomes are there if three coins are tossed?

thx

iamthetman

Try listing out the possibilities:

Heads, Heads, Heads
Heads, Heads, Tails
Heads, Tails, Heads
Heads, Tails, Tails
Tails, Heads, Heads
Tails, Heads, Tails
Tails, Tails, Heads
Tails, Tails, Tails

Lowtax4eva

Although were not supposed to do your homework for you its 6... only answering because the above is wrong:

Tails, Heads, Tails
Tails, Tails, Heads

These 2 are the same

iamthetman

Actually my answer is not wrong. The key here is whether or not the order of the coins matters.

If order matter then there are 8 possible outcomes. If order doesn't matter then there are 4 possible outcomes.

morgaine300

Lowtax4eva, iamthetman is actually correct. This is a weird concept to learn, but each coin is a separate event and each has to be figured separately.

Tails, Heads, Tails means the first coin landed tails, the second landed heads and the third landed tails.

Tails, Tails, Heads means the first coin landed tails, the second landed tails and the third landed heads.

Those are two different sets of outcomes and are not the same.

Original poster, another method is multiplication. Take each step, i.e. the toss of a coin, and figure the number of outcomes it can have. Multiply the outcomes.

That is, the first thing you will do is toss one coin. It has two outcomes: heads and tails. Then you are going to do a second thing. Toss another coin. It does not matter that the second thing you're doing is the same as the first thing. You're doing it again, so you have to figure it again. And it has two outcomes: heads and tails. Then you're doing a third thing, tossing another coin. And it has two outcomes: heads and tails.

Each step has 2 possible outcomes. Multiply the outcomes of each of the three: 2 x 2 x 2 = 8 total possible outcomes for the experiment. Same answer as when you list the outcomes like iamthetman did.

Even though this doing the same thing 3 times, it is no different than making a sandwich. First step is picking the bread: white, wheat or rye. (3 outcomes) Second step picking a condiment: mayo or mustard. (2 outcomes) Third step picking a meat: turkey or ham. (2 outcomes) 3 x 2 x 2 = 12 total possible outcomes for the sandwich making. The coin toss is exactly the same.

MaggieMouse

Are these identical coins? If they are then the sandwich example above is incompariable.

galactus

Assuming fair coins and all that, there are 2^n possible outcomes when tossing n coins.

Order matters is assumed with these coin tossing problems.

There would be 2^3=8 outcomes if 3 were tossed.

There would be 2^10=1028 if 10 coins were tossed.

There would be 2^1000 if 1000 were tossed.

And so on.