Question

You and a friend are rolling a set of 5 dice. The game works such that if a die shows the values 1, 2, 3, or 4 you will get a point for that die. Each die that shows 5 or 6 your friend will get a point for. Construct a probability model for a single roll of the dice then answer the following.

Step 1 of 5:

What is the probability you made 2 points?

Step 2 of 5:

What is the probability that your friend will score 2 points?

Step 3 of 5:

What is the probability you score 4 or more points in this round?

Step 4 of 5:

If we play a second round of this game, what is the probability that you will have exactly 6 points at the end of the second round?

Step 5 of 5:

If we play another round what is the probability you will have 10 or more points?

Answer 1

#1.
probability of getting 1, 2, 3 or 4 on any die is 4/6

In order to earn 2 points exactly 2 dice should show 1, 2 ,3 or 4

required probability = 5C2 * (4/6)^2 * (2/6)^3 = 0.1646

#2.
probability of getting 5 or 6 on any die is 2/6

In order to earn 2 points exactly 2 dice should show 5 or 6

required probability = 5C2 * (2/6)^2 * (4/6)^3 = 0.3292

#3.
in order to score 4 or more points, 4 or more dice should show 1,2,3 or 4

required probability = (5C4 * (4/6)^4 * (2/6) + 5C5 * (4/6)^5 * (2/6)^0) = 0.4609

#4.
second round means overall 10 dice are rolled

required probability = 10C6 * (4/6)^6 * (2/6)^4 = 0.2276

#3.
aother round means overall 15 dice are rolled

required probability = 15C10 * (4/6)^10 * (2/6)^5 = 0.2143