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Two dice are rolled.  Find the probability of gettingA. A sum of 5,6,7B. Doubles or sum of 6 or 8C. A sum greater than 8 or less than 3D Based on the answers to parts a, b, c which is least likely to occur? explain why?

Question

Two dice are rolled.  Find the probability of getting

A. A sum of 5,6,7

B. Doubles or sum of 6 or 8

C. A sum greater than 8 or less than 3

D Based on the answers to parts a, b, c which is least likely to occur? explain why?

check_circleAnswer
Step 1

Sample space for rolling two dice:

It is given that two dice are rolled. The number of possible outcomes for rolling two dice is 36. The sample space is as follows.

(1, 1) (, 2) (, 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)
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(1, 1) (, 2) (, 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)

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Step 2

A. Probability of getting a sum of 5,6,7:

The probability of getting a sum of 5,6,7 is P5 + PP7

The possible outcomes for which the pair sum is 5 in the total of 36 outcomes are (1, 4), (2, 3), (3, 2), (4, 1). Thus, there are 4 favorable outcomes for which the pair sum is 5.

The possible outcomes for which the pair sum is 6 in the total of 36 outcomes are (1, 5), (2, 4), (3, 3), (4, 2), (5, 1). Thus, there are 5 favorable outcomes for which the pair sum is 6.

The possible outcomes for which the pair sum is 7 in the total of 36 outcomes are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). Thus, there are 6 favorable outcomes for which the pair sum is 7.

The probability of getting a sum of 5,6,7 is 0.4167 from the calculations given below.

Number of favorable outcomes
Probability tal number of possible outcomes
4
36
36
6
36
4 56
36
15
36
=0.4167
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Number of favorable outcomes Probability tal number of possible outcomes 4 36 36 6 36 4 56 36 15 36 =0.4167

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Step 3

B. Probability of getting doubles or sum of 6 or 8 Probability of getting doubles or sum of 6 or 8:

The possible outcomes of getting doubles are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6). Thus, there are 6 favorable outcomes.

The possible outcomes of getting a sum of 6 or 8 are (1, 5), (2, 4), (2, 6), (3, 3), (3, 5), (4, 2...

6 10 2
P =
36
14
36
=0.3889
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6 10 2 P = 36 14 36 =0.3889

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