Heads or Tails (are you a genius)?

Question

Heads or Tails
by Jeffrey Stapleton

I have two quarters, one is a double sided heads and the other is a regular quarter. I select one at random of the two, and flip it in the air and it comes up heads. What are the odds the other side of this quarter is also heads?

Expalin your answer fully

Rowan D's was correct first.

Answer 1

I'm not very good at explanation, but here goes.

Imagine you take your 2 coins and number the sides of them:

The tail/head coin you number tail 1, and head 2
The head/head coin you number one head 3, and the other 4.

So if you randomly grab a coin and toss it 3/4 of the time it will be heads.
(you know that already)

Now that the coin has come up heads, it could be numbered 2, 3 or 4. On 2 of these results there is a head on the reverse, on 1 there is a tail.
So the odds there is a tail on the reverse is 1 in 3, or 33.333.%
and the odds there is a head on the reverse is 2 in 3, or 66.666%

How'd I do?

These numb nuts that go "It's one coin or the other" aren't thinking through the number of possible results!

Answer 2

The probability that it is the double coin, knowing that the flip came up heads is equal to the probability that it is the double coin divided by the probability that it is heads.

The probability that is is the double coin: 1/2
The probability that it came up heads: 3/4

Therefore the probability that the other side is heads (or that it was the double coin), given that it came up heads: (1/2)/(3/4)=2/3


This can be figured by listing the possibilities also:
Let the coin with two heads have sides A1 and A2. Let the coin with a head and a tail have BH (heads) and BT (tails). The possible outcomes are:
{A1, A2, BH, BT}

The possible outcomes with a head are
{A1, A2, BH}.

of these, two of them are from the coin with the double heads, and only one is from the regular coin. therefore there is a 2/3 probability that the other side is a head.

And apparently some people are out smarted by a three year old . . .

Answer 3

there is a 50% possibility that you picked up the 2 headed coin & a 100% chance that you will get heads if you do. There is a 50% that you picked up the regular coin & you have a 50% chance of getting heads if you do.
There is a 50%*100% +50%*50%=75% chance that you wil get heads.

Since there is a 50% chance that you picked up the 2 headed coin, your odds that the flip side is heads is:
50%/75%=67%

Answer 4

I would say you have a 66 percent chance because you have three heads in all and one tail so you only have two heads left and one tail and since we have decided that you landed on heads that leaves 2 heads left out of 3 sides, so I am going with 66%

Answer 5

50

Answer 6

[combinations possible

coin1 head ,coin 1 tail

coin 1 tail and coin 1 head

coin 2 head coin 2 head

coin 2 head coin 2 head]

First one is necessarily head so total possibilities become 3.

Favourable are second one with head too.

That gives 2 possiblities ]

P(a) = favoured/total
= 2/3

So add are 3:2

Answer 7

Heads, i will not answer; tails i will answer. Oh!! i just got a tail; you might be right this time... but i will prove you wrong because i am a Ray Of Light. haha

Answer 8

P (head) = 1/2.


Are you trying to confuse us with your half and quarter thing? It's a simple probability imo. Just calculate the probability accordingly. Either you get the one with 2 heads or the one with no head.

Answer 9

ok sounda probablity ok
.5 probality for a doubble headed coin and it is not the side u wana calculate for pro but it is ony the coin so it is the .5 ie 50% chance

Answer 10

Most problems in probability are all about how the question is phrased.
Congrats on being so sneaky. ;)