You roll two die. What is the probability of rolling a 1 and a number that is at most 3?

Answer 1

If order does not matter, getting a 1 AND another number that is at most 3:

1, 1

1, 2

2, 1

1, 3

3, 1

NOTE that 2, 2 should not be counted, since there is no 1 in this pair.

Total possibilities when rolling 2 dice is 36.

5/36 if order does not matter.

If order does matter;

1, 1

1, 2

1, 3

3/36 = 1/12.

Answer 2

roll 2 dice

probability of rollng 1 and at most 3 = 1/6

unless order matters

= P(1 & 1,2 or 3) = 3(1/36) = 1/12

P(1,1) = 1/6 x 1/6 = 1/36

P(1,2) = 1/36

P(1,3) = 1/36

P(1,1) or P(1,2) or P(1,3) = 1/12

if order matters, 1 on 1st die, 1,2,or 3 on 2nd die

P(1) = 1/6

P(1,2 or 3)= 1/2

1/6x1/2 = 1/12

but if order doesn't matter, if 1st die can be 1,2 or 3 and 2nd die 3,2 or 1

then P(<5 for sum of both dice)= 6/36=1/6

1,1 happens only 1 way sum =2

1,2 or 2,1 happens 2 ways sum=3

1,3, 3,1 or 2,2 happens 3 ways sum =4

36 different ways to get sum of 2 through 12 for the 2 dice, 6 ways to get sum of 2,3 or 4

(1+2+3)/36 = 6/36, but subtract 1/36 as 2,2 has no one oneither dice,

leaving 5/36

sum ways

2 1

3 2

4 3

5 4

6 5

7 6

8 5

9 4

10 3

11 2

12 1

total ways = 1+2+3+4+5+6+5+4+3+2+1=36

ways to get <5 = 1+2+3 = 6

probability of less than 5 = ways to get less than 5 divided by total ways