In the game Yahtzee, five fair 6-sided dice are rolled.
a. What is the probability of rolling exactly three 1s?
b. What is the probability of rolling exactly three of any number?
c. What is the probability of rolling three, four, or five of a kind?
This question has taken me completely by surprise. The book never talked about any of this question and it has taken me hours of thinking to find nothing.
Hello, krzyrice!
These are from the topic "Binomial Probability."
You should be familiar with the formula.
noob explained this nicely.In the game Yahtzee, five fair 6-sided dice are rolled.
a. What is the probability of rolling exactly three 1s?
b. What is the probability of rolling exactly three of any number?
Since there are six choices for the value of the 3-of-a-kind,
. . the probability is six times the answer in part (a).
We already know that: .c. What is the probability of rolling three-, four-, or five-of-a-kind?
Four-of-a-kind: 4 of one number, 1 of another.
There are 6 choices for the quadruple.
. .
Five-of-a-kind: 5 of one number.
There are 6 choices for the quintuple.
. .
Therefore: .