Question

Question #59f14

Answer 1

`~~29%`

Explanation:

You can only get 3 distinct combinations using 3 coins. Either 1 head and two tails, 2 heads and 1 tail or 3 heads. Below are the possible configurations

`1 -> 1,0,0 |0,1,0|0,0,1` each person can result in `3 times3=9`
`2-> 1,1,0 |0,1,1|1,0,1` each person can result in `3 times3=9`
`3-> 1,1,1` each person can result in `1 times1=1`

The total amount of combinations between the 2 coins is `2^6` because a coin has two options either heads or tails. If both have 3 coins this amounts to 6 total combinations of heads or tails.

Thus `19/2^6=.296875 ~~29.69%`

This simulation confirms the results using R

n<-0;
t<-100000;
for(i in 1:t)
{
boy1<-round(runif(3,0,1));
boy2<-round(runif(3,0,1));
if(sum(boy1)==sum(boy2) && sum(boy1)>0){n=n+1;}
}
n/t

this resulted in 0.29444