Chapter 15.3, Problem 12P

(a) A loaded die has probabilities $\frac{1}{21},\frac{2}{21},\frac{3}{21},\frac{4}{21},\frac{5}{21},\frac{6}{21},$ of showing 1,2,3,4,5,6

What is the probability of throwing two 3 ’s in succession?

(b) What is the probability of throwing a 4 the first time and not a 4 the second time with a die loaded as in (a)?

(c) If two dice loaded as in (a) are thrown, and we know that the sum of the numbers on the faces is greater than or equal to 10, what is the probability that both are 5 ’s?

(d) How many times must we throw a die loaded as in (a) to have probability greater than $\frac{1}{2}$ of getting an ace?

(e)A die, loaded as in (a), is thrown twice. What is the probability that the number on the die is even the first time $>4$ the second time?