Description

Arnab Dey
Student ID: 5563169
Email: dey00011@umn.edu
Solution 1.a
As each of the 5 di erent colored dice can have 12 di erent numbers, the total number of atomic events is
125.
Solution 1.b
The probability of each atomic event is .
Solution 1.c
We can choose any one number from 12 di erent numbers. Then, for that number, we can choose 3 di erent colors out of 5. After, choosing the rst number, we will be left with 11 numbers from which we have to choose one. Then for this number, we can choose 2 out of 5 di erent colors. Therefore, the total number of events are:
Total number of events .
Therefore, the probability of rolling a full house is .
Solution 1.d
For four of a kind, we can choose any one number out of 12, then for this number we can choose any 4 colors out of 5. The other number can be chosen from 11 di erent numbers and for this number we will have choice of 1 color out of 5 di erent colors. Therefore, the total number of events are:
Total number of events .
Therefore, the probability of four of a kind is .