Suppose that a die is loaded so that the probability of roll

Suppose that a die is loaded so that the probability of rolling a number is proportional to that number. What is the probability of rolling 5?

Solution

When we roll a die then possible outcomes are 1, 2, 3, 4, 5, 6. Let X shows the outcome of teh die. Here we need 1+2+3+4+5+6=21. Since the probability of rolling a number is proportional to that number so

P(X=1) = 1/21

P(X=2) = 2/21

P(X=3) = 3/21

P(X=4) = 4/21

P(X=5) = 5/21

P(X=6) = 6/21

That is if we roll die 21 times, we can expect outcome 1 comes 1 time, outcome 2 comes 2 times and so on.

So the probability of rolling 5 is 5/21.