# Thread: Question Involving Both a Die and Coin

1. ## Question Involving Both a Die and Coin

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.

2. ## Re: Question Involving Both a Die and Coin

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

3. ## Re: Question Involving Both a Die and Coin

Originally Posted by Dason
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...

5. ## Re: Question Involving Both a Die and Coin

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!

6. ## Re: Question Involving Both a Die and Coin

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?

7. ## The Following User Says Thank You to Dason For This Useful Post:

S-C-3-1-3 (09-10-2012)

8. ## Re: Question Involving Both a Die and Coin

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).

9. ## Re: Question Involving Both a Die and Coin

Originally Posted by 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?
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.

10. ## Re: Question Involving Both a Die and Coin

Originally Posted by 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).
The question does not indicate that order matters. It only asks the possible outcomes.

11. ## Re: Question Involving Both a Die and Coin

Originally Posted by 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?
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?

12. ## Re: Question Involving Both a Die and Coin

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

13. ## Re: Question Involving Both a Die and Coin

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.

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