Question

1. Suppose you have a fair 6-sided die with the numbers 1 through 6 on the sides and a fair 5-sided die with the numbers 1 through 5 on the sides. What is the probability that a roll of the six-sided die will produce a value larger than the roll of the five-sided die?
2. What is the expected number of rolls until a fair five-sided die rolls a 3?

Answer 1

Answer:

a. 0.5 or 50%

b. 5 rolls.

Step-by-step explanation:

a. There are 30 possible outcomes for this experiment, the sample space for the outcomes in which the six-sided die produces a value larger than the roll of the five-sided die is:

S={6,1; 6,2; 6,3; 6,4; 6,5; 5,1; 5,2; 5,3; 5,4; 4,1; 4,2; 4,3; 3,2; 3,1; 2,1}

There are five outcomes when rolling a 6, four when rolling a 5, three when rolling a 4, two when rolling a 3 and one when rolling a two.

The probability is:

$P = \frac{5+4+3+2+1}{5*6}=0.5$

b. The probability of rolling a 3 on the five-sided die is 1 in 5 or 0.20. The expected number of rolls until a fair five-sided die rolls a 3 is:

$E(x=1) = \frac{1}{p(x)}=\frac{1}{0.2}= 5\ rolls$