Math Gurus?

[CHCRandy]

If you have 2 quarters and a dice........what is the probability that you will roll a 6 while flipping both heads on the quarters?

Can you kind of tell me how you figured it as well?

 

[pudly]

Pretty simple case actually. I'm assuming you mean a basic six-sided die.

1/6 * 1/2 * 1/2 = 1/24 or 4.17%.

Since each event is independent, you multiply the probabilities of each.

 

[CHCRandy]

Pretty simple case actually. I'm assuming you mean a basic six-sided die.

1/6 * 1/2 * 1/2 = 1/24 or 4.17%.

Since each event is independent, you multiply the probabilities of each.

That wasn't one of the answers though....it is multiple choice. That was my first answer. This is some kind of test my daughter is taking in one of her college classes. She asked me......and I couldn't figure it out. I got the 1/6...but the 2 quarters could be heads/heads, head/tail, tail/tail, tail/head. So if you have them 4 combinations....with only 1 desirable outcome and 3 undesirable......wouldn't that be 1/4? Not doubting you....but is there anyway it could be 1/12? I mean if I think about that....you could have heads/tail with a 1, 2, 3, 4, 5, 6. Then tail/heads with a 1, 2, 3, 4, 5, 6. Then tail/tail 1, 2, 3, 4, 5, 6. Then heads/heads 1, 2, 3, 4, 5. That sure looks like it would add up to 1/24........but that isn't a choice. 1/12 is a choice though....

Thanks for your help.

 

[pudly]

Yes, 2 heads on two coins is 1/4 chance (1/2 * 1/2 above). If the problem is exactly as you described, then the answer is 1/24. You listed all 24 possibilities above and they are all equal probability. Note that there are two ways to get 1 head and 1 tail. That means that you have 2 * 1/24 = 1/12 chance to get a 6 + 1 head + 1 tail. 1/24 to get a 6 and two heads . 1/24 to get a 6 and 2 tails, etc.

 

[Mr Evilwrench]

Pudly is right, the choices aren't multiple enough.

 

[IndyDave1776]

Never take the answer in the book for holy writ. I recall a time I was helping someone prepare for the GED test, working with a geometry problem. I explained the problem in a way that made sense, all was happy, and then she looked in the back of the book and found a different answer. I then had to show her how to get the answer in the book and then explain why and how they had mathematically derived a correct answer, but while technically correct, their answer did NOT answer the question being asked. It sounds like you have a similar situation on your hands. Pudly explained the math adequately and correctly. Always remember that the book is NOT infallible!

 

[Bigtanker]

How to Determine Probable Outcomes with Coins and Dice - For Dummies

 

[ccomstock001]

I think 1/12 is right because you still have a 50% probability of getting heads on both. You still have a 2 out of 4 chance on the quarters which reduces to 1/2.

 

[Snapdragon]

What is the exact wording of the question? Is it as you wrote it in the OP?

 

[Snapdragon]

I think 1/12 is right because you still have a 50% probability of getting heads on both. You still have a 2 out of 4 chance on the quarters which reduces to 1/2.

You don't have a 2/4 chance on the quarters. The possibilities are HT HH TH TT, so HH is 1/4.

 

[Snapdragon]

You don't have a 2/4 chance on the quarters. The possibilities are HT HH TH TT, so HH is 1/4.

Unless, they are counting the three possibilities as two heads, two tails, and one head/one tail. (Bogus, but whatever.) That would make it 1/3 * 1/6 = 1/18 or 5.56%. Is that one of the choices?

 

[ccomstock001]

Unless, they are counting the three possibilities as two heads, two tails, and one head/one tail. (Bogus, but whatever.) That would make it 1/3 * 1/6 = 1/18 or 5.56%. Is that one of the choices?

I don't know what I was thinking. And I don't think it would be too bogus because ht and th is the same result I don't think the order would matter

 

[Snapdragon]

Yeah, it depends on whether order matters or not and that wasn't made clear. I think the crux is whether they are counting HT the same as TH (combination) or HT as different from TH (permutation).

 

[CHCRandy]

Yeah, it depends on whether order matters or not and that wasn't made clear. I think the crux is whether they are counting HT the same as TH (combination) or HT as different from TH (permutation).

The daughter has done went to bed...so not sure how it was worded exactly. I thought it said if you have 2 coins and a 6 sided numbered square what is the probability of flipping 2 heads and rolling a 6? It's funny because I originally said 1/3 on the coins......then my daughter convinced me there were 4 ways. 1/18 was not a choice.

 

[IndyDave1776]

Yeah, it depends on whether order matters or not and that wasn't made clear. I think the crux is whether they are counting HT the same as TH (combination) or HT as different from TH (permutation).

Good catch. I, for one, had overlooked that.

In my case, I am not entirely surprised that I would have an issue with a game of chance. After all, a couple of years ago at our Christmas party, some gambling for chips (no cash value) broke out. My co-workers gave me one piece of advice: Stay away from the boat (casino)!

 

[Redtbird]

Owww! My head hurts now! Interesting question tho!

 

[9mmfan]

Makes me glad I never went higher than Algebra II.

Or maybe I should have forced myself to go higher.

 

[MilliJac]

Unless, they are counting the three possibilities as two heads, two tails, and one head/one tail. (Bogus, but whatever.) That would make it 1/3 * 1/6 = 1/18 or 5.56%. Is that one of the choices?

For the question asked in OP this wouldn't matter, it would still be a 1/2 x 1/2 = 1/4 chance for the 2 coins.

 

[femurphy77]

I'm still working on the train coming from one direction and the low rider coming from the other direction. . . .

 

[BugI02]

The 1/24 possibility would be correct if the events making up the sequence were required to happen in a particular order. Since they are not the result is divided by 3 factorial (3 x 2 x1) which gives the number of possible orders the three events can happen in. And in this case that result (6) is divided by 2 because which quarter is used when is immaterial. The ways of completing the sequence are Q,Q,D Q,D,Q OR D,Q,Q. Q1,Q2,D is the same as Q2,Q1,D
for the purpose of this sequence. Thus it is 1 over [24 div (6 div 2)]. Was 1/8 an option?