Consider the following experiment First you roll a fair die

Consider the following experiment. First, you roll a fair die. If a 6 comes up, let X=0; otherwise, toss a fair coin three times and let X equal the number of heads that show. Now suppose someone did that experiment and the resulting value of X was 0. What is the probability that a 6 came up on the die?

Solution

Well if x=0 then a 6 comes up

if you roll a fair die, the die can take values of 1,2,3,4,5,6 we have 6 posibles cases for this experimient

but if the result is a 6 how many 6 are in the experiment? only 1 right?

so the favorables cases for a 6 came up on the die is 1

so the probability is defined by the division of FAVORABLES CASES / POSIBLES CASES

WE CONCLUDE THAT

THE PROBABILITY THAT A 6 CAME UP ON THE DIE = 1/6