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.

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,