-faced die is tossed twice. Letting E and F represent the outcomes of the two A

Question

-faced die is tossed twice. Letting E and F represent the outcomes of the two A fair 6-faced die is tossed twice. I tosses, comp (a) The sum of E and Fis 11. (b) The sum of E and Fis even. 14-4 ute the following probabilities: The sum of E and F is odd and greater than 3. E is even and less than 6, and F is odd and greater than 1. (e) E is greater than 2, and F is less than 4. (o E is 4, and the sum of E and F is odd .5. Two dice are rolled independently, and the two numbers that turn up are recorded. Determine the following: (a) The probability that the two numbers are even (b) The probability that the sum of the two numbers is 10. (c) The probability that the two numbers differ by at least 3.

Explanation / Answer

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

S = { 2, 3, 4, 5, 6, 7

3, 4, 5, 6, 7, 8

4, 5, 6, 7, 8, 9

5, 6, 7, 8, 9, 10

6, 7, 8, 9, 10, 11

7, 8, 9, 10, 11, 12

a) there are two instances when sum is equal to 11

P(sum is 11) = 1/18

b)half of the instances are with even sum

P(sum is even) = 1/2

c)there are 16 instances when sum is odd and greater than 3

P(required) = 4/9

d) There are only 4 instances when E is even and less than 6 and F is odd and greater than 1.

P(required) = 4/36 = 1/9

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