Question

A red 20-sided die, with faces marked from 1 to 20 , is rolled. The result is denoted by D1 . Then a green 20-sided die, similarly marked, is rolled. The result here is denoted by D2 .

1) What is the probability that the value 6 shows up on at least on of the rolls? P(D1=6∪D2=6)

2) What is the probability that the value 6 show up on exactly one of the rolls? P((D1=6∪D2=6)∖(D1=6∩D2=6))

3) What is the probability (as a rational number is a/b format) that the value sum D1+D2 is 30 ? 10 ? 23 ?
P(D1+D2=30)
P(D1+D2=10)
P(D1+D2=23)

Answer 1

1)

If the value 6 appears on at least one of the dice, then it would be easier to calculate the probability of 6 not appearing at all.

19/20 * 19/20 = 361/400

1- 361/400 =

39/400

2) If 6 only shows up on one of the dice, this leaves two possibilities. D1 = 6 and D2 = other, or D1 = other and D2 = 6

(19/20 * 1/20) + (1/20 * 19/20) =

38/400

3) The numbers that equal 30 together =

20 , 10

19 , 11

18 , 12

17, 13

16,14

15,15

14,16

13,17

12,18

11,19

10, 20

= 11 possibilities

in each case the probability of getting those 2 numbers = 1/20 * 1/20 = 1/400

= 1/400 * 11 = 11/400

----

For number 10 we have:

1, 9

2,8

3,7

4,6

5,5

4,6

3,7

2,8

1,9

= 9 possibilities

= (1/20 * 1/20) * 9 = 9 /400

----

For 23

= 20 , 3

19, 4

18, 5

17, 6

16, 7

15, 8

14, 9

13, 10

12, 11

11, 12

10, 13

9, 14

8, 15

7, 16

6, 17

5, 18

4, 19

3,20

= 18 possibilities

repeat the steps above, you have 18/400