Question Involving Both a Die and Coin

[S-C-3-1-3]

Hi,

I am having difficulties with this probability question and would love some feedback to see if I am thinking this through correctly: “A die is rolled and then a number of coins equal to the number showing on the die are tossed. What is the number of possible outcomes of the two experiments?”
I think it would be 6 x 6 x 2 = 72 possible outcomes, because there could be 6 possible outcomes of the die rolling, which means there could be up to 6 coins tossed, and each can be either heads or tails, thus 2 possible outcomes.

Thanks in advance!

[Dason]

This isn't correct. Also note that if you flip 6 coins there are not just 6x2 = 12 possible outcomes.

[S-C-3-1-3]

This isn't correct. Also note that if you flip 6 coins there are not just 6x2 = 12 possible outcomes.

Could you explain? The following would be the possible outcomes for 6 tossed coins:

TH TH TH TH TH TH.

Please tell me where I am wrong, thanks...

[BGM]

http://en.wikipedia.org/wiki/Rule_of_product

[S-C-3-1-3]

http://en.wikipedia.org/wiki/Rule_of_product

Hi,

I reviewed the article you sent me.

I figure now that the answer is 6 x 64 = 384 possible outcomes, because there are 6 possible outcomes when rolling one die die and 64 possible outcomes when rolling a coin 6 times (2 x 2 x 2 x 2 x 2 x 2).

Is this right?

Thank you, by the way, for your help!

[Dason]

That assumes that there are 64 outcomes regardless of what was rolled on the die. How many outcomes are there for the coin flips if a 1 is rolled on the die?

[lancearmstrong1313]

Does the order of the coin flip matter? For example, is flipping a Head then a Tail equal to flipping a Tail then a Head? I'm not sure if the question implied all coins are flipped at once (in which order would probably not matter) or one at a time (in which order would probably matter).

[S-C-3-1-3]

That assumes that there are 64 outcomes regardless of what was rolled on the die. How many outcomes are there for the coin flips if a 1 is rolled on the die?

If a 1 is rolled on the die, there would be two possible outcomes, correct? For, 1 x 2 = 2, correct? Would I, therefore, add all of the individual possibilities? For example, add the possible outcomes if a 1 is tossed, 2 is tossed, 3 is tossed, etc.

[S-C-3-1-3]

Does the order of the coin flip matter? For example, is flipping a Head then a Tail equal to flipping a Tail then a Head? I'm not sure if the question implied all coins are flipped at once (in which order would probably not matter) or one at a time (in which order would probably matter).

The question does not indicate that order matters. It only asks the possible outcomes.

[S-C-3-1-3]

That assumes that there are 64 outcomes regardless of what was rolled on the die. How many outcomes are there for the coin flips if a 1 is rolled on the die?

Hi,

I think I now understand. I need to add the possible outcomes for rolling a 1, 2, 3, 4, 5, and 6. Therefore, 2 + 4 + 8 + 16 +32 +64 = 126 possible outcomes.

Is this correct?

[lancearmstrong1313]

Assuming order does not matter

If you roll a 1, then you flip one coin - there are 2 possible outcomes.

If you roll a 2, then you flip two coins (TT, HH, 1 Head/1 Tail) - there are 3 possible outcomes

If you roll a 3, then you flip three coins (3 Heads, 2 Heads/1 Tail, 1 Head/2 Tails, 3 Tails) - there are 4 possible outcomes

If you roll a 4, then you flip four coins (4 Heads, 3 Heads/1 Tail, 2 Heads/2 Tails, 1 Head/3 Tails, 4 Tails) - there are 5 possible outcomes
...
...

So rolling a 1 -> 2 outcomes
rolling a 2 -> 3 outcomes
rolling a 3 -> 4 outcomes
rolling a 4 -> 5 outcomes
rolling a 5 -> 6 outcomes
rolling a 6 -> 7 outcomes

Thus, there would be 2+3+4+5+6+7 = 27 possible outcomes


Assuming order does matter

If you roll a 1, then you flip one coin - there are 2 possible outcomes.

If you roll a 2, then you flip one coin twice - there are 2*2 possible outcomes (4)

If you roll a 3, then you flip one coin three times - there are 2*2*2 possible outcomes (16)

If you roll a 4, then you flip one coin four times - there are 2*2*2*2 possible outcomes (32)
...
...

So rolling a 1 -> 2 outcomes
rolling a 2 -> 4 outcomes
rolling a 3 -> 8 outcomes
rolling a 4 -> 16 outcomes
rolling a 5 -> 32 outcomes
rolling a 6 -> 64 outcomes

Thus, there would be 2+4+8+16+32+64 = 126 possible outcomes

[Dason]

Depends on what you're referring to as outcomes. Sometimes the order of Heads/Tails does matter and since the OP didn't mention this I take that to mean that H,T is different than T,H.