# Question 59f14

Jul 21, 2016

~~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

$1 \to 1 , 0 , 0 | 0 , 1 , 0 | 0 , 0 , 1$ each person can result in $3 \times 3 = 9$
$2 \to 1 , 1 , 0 | 0 , 1 , 1 | 1 , 0 , 1$ each person can result in $3 \times 3 = 9$
$3 \to 1 , 1 , 1$ each person can result in $1 \times 1 = 1$

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