Question #59f14

1 Answer
Will
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 -> 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

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