Two People flip a coin, Each person flips it 50 times, Each person then counts the number of heads, What is the probability they both get the same number of heads?
I don't see an easy way to do this, as there are 50 different numbers of heads.
Pr(1)=(.5)^1(.5)^49
and the Q(r) the second person is the same, so the joint probability that both will get only one H is
Pr(1,1)=(.5)^2(.5)^98 =(.5)^100
Now, Pr(2,2)=(.5)^4(.5)^96=.5^100
and Pr(3,3)=(.5)^6(.5)^94=.5^100
so you have to sum all these up, from 0.0 to 50,50
as in Pr(0,0)=.5^0*.5^100+(pr(1,1)=.5^100 + ....+Pr(50,50)=.5^100
That is 51 times, or
Pr(total, total same)=51*.5^100
check my thinking
To find the probability that both people get the same number of heads, we need to consider all possible outcomes for each person flipping the coin 50 times.
The total number of possible outcomes for flipping a coin 50 times is 2 raised to the power of 50, since each coin flip has two possible outcomes (heads or tails). So, there are 2^50 possible outcomes for each person.
Let's first consider the number of ways each person can get the same number of heads:
- Person A can get 0 heads, Person B can also get 0 heads (1 way).
- Person A can get 1 head, Person B can also get 1 head (1 way).
- Person A can get 2 heads, Person B can also get 2 heads (1 way).
- And so on, up to 50 heads.
Since there are 51 possible outcomes where both people get the same number of heads, the probability of this happening is 51 divided by the total number of possible outcomes (2^50).
So, the probability that both people get the same number of heads is:
51 / (2^50)