Question

You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 7? (Enter your answer as a fraction.) 1/6 Correct: Your answer is correct. (b) What is the probability of getting a sum of 11? (Enter your answer as a fraction.) 1/18 Correct: Your answer is correct. (c) What is the probability of getting a sum of 7 or 11? (Enter your answer as a fraction.) 2/9 Correct: Your answer is correct. Are these outcomes mutually exclusive?

Answer 1

Answer:

a) 0.167  b)0.056  c)0.023

Step-by-step explanation:

We are given the following information:

Sample space = {(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)}

Total number of outcomes = 36

Formula:

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

a) P(sum is 7)

Sum 7 possible outcomes = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

$= P = \displaystyle\frac{6}{36} = \displaystyle\frac{1}{6} = 0.167$

b) P(sum is 11)

Sum 11 possible outcomes = {(5,6), (6,5)}

$= P = \displaystyle\frac{2}{36} = \displaystyle\frac{1}{18} = 0.056$

c) P( sum is 7 or sum is 11)

$= P(\text{sum is 7}) + P(\text{sum is 11}) - (P(\text{sum is 7}\cap \text{sum is 11})) \\= \displaystyle\frac{6}{36} + \displaystyle\frac{2}{36} + 0\\\\= \displaystyle\frac{8}{36} = \displaystyle\frac{2}{9} = 0.223$