# Probability of getting different results when tossing a coin

#### Yotam Ohayon

##### New Member
Here's a question I got for homework:
In every single time unit, Jack and John are tossing two different coins with P1 and P2 chances for heads. They keep doing so until they get different results. Let X be the number of tosses. Find the pmf of X (in discrete time units). What kind of distribution is it?
Here's what I have so far: In every round (time unit) the possible results
HH - p1p2
TT - q1q2
TH - q1p2
HT - q2p1
and so
P(X=k) = ((p1p2 + q1q2)^(k-1))*(q1p2+q2p1)
Which means we're dealing with a geometric distribution.

What doesn't feel right is that the question mentions 'discrete time units'. That makes me think about a Poisson distribution, BUT - Poisson is all about number of successes in a time unit, while here we only have one round in every time unit.

If I'm not too clear its only because I'm a little confused myself. Any hint would be perfect. Thanks in advance

#### BGM

##### TS Contributor
Sorry not sure what thing confused you.

I think the question just emphasize:

1. Two coins are tossed at the same time (unit)

2. It is a discrete distribution.

#### Yotam Ohayon

##### New Member
Sorry not sure what thing confused you.

I think the question just emphasize:

1. Two coins are tossed at the same time (unit)

2. It is a discrete distribution.
Well, its either a geometric distribution or a Poisson distribution, but it couldn't be both. I think its a geometric one, but then what does time units have to do with it?

#### BGM

##### TS Contributor
I agree it is a geometric distribution. Not sure why you think it is related to Poisson distribution.

Also I do not know why the question used the term "time unit" several times. Anyway I think the main point is "Let X be the number of tosses. "