Two dice are rolled. Find the probability of getting a. A sum of 5, 6, or 7 b. Doubles or a sum of 6 or 8 c. A sum greater than 8 or less than 3 d. Based on the answers to parts a, b, and c, which is least likely to occur

The answer is below

Step-by-step explanation:

The possible outcome from rolling two dice is:

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

The total number of outcomes = 36

a)

P(sum of 5) = 4/36, P(sum of 6) = 5/36, P(sum of 7) = 6/36

Hence:

P(sum of 5 or sum of 6, or sum of 7) = P(sum of 5) + P(sum of 6) + P(sum of 7) = 4/36 + 5/36 + 6/36

P(sum of 5, 6, or 7) = 15 / 36

b)

P(doubles) = 6/36, P(sum of 6) = 5/36, P(sum of 8) = 5/36

Hence:

P(doubles or sum of 6 or sum of 8) = P(doubles) + P(sum of 6) + P(sum of 8) = 6/36 + 5/36 + 5/36

P(doubles or sum of 6 or sum of 8) = 16 / 36

c)

P(sum greater than 8) = 10/36, P(sum lesser than 3) = 1/36

P(sum greater than 8 or less than 3) = P(sum greater than 8) + P(sum lesser than 3) = 10/36 + 1/36

P(sum greater than 8 or less than 3) = 11 / 36

Part c has the least probability of occurrence, hence c is least likely to occur.

answer:   n ≤ -3 or n < -5

step-by-step explanation:

-5 + 2n ≥ -11

+5             +5

2n ≥ -6

2/2 ≤ -6/2

n ≤ -3

-6 - 10n > 44

+6           +6

-10n > 50

-10/-10 50/-10

n < -5

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.