A pair of dice is rolled once. (a) Find the probability of rolling a 10. (Enter your answer as a fraction.) (b) Find the probability of rolling a 10 given that the number rolled is even. (Enter your answer as a fraction.) (c) Are the events "rolling a 10" and "rolling an even number" independent? Why? Yes, the probabilities in (a) and (b) are the same. No, the probabilities in (a) and (b) are different.

A pair of dice is rolled once. (a) Find the probability of rolling a 10. (Enter your answer as a fraction.) (b) Find the probability of rolling a 10 given that the number rolled is even. (Enter your answer as a fraction.) (c) Are the events "rolling a 10" and "rolling an even number" independent? Why? Yes, the probabilities in (a) and (b) are the same. No, the probabilities in (a) and (b) are different.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A pair of dice is rolled once.

(a) Find the probability of rolling a 10. (Enter your answer as a fraction.)

(b) Find the probability of rolling a 10 given that the number rolled is even. (Enter your answer as a fraction.)

(c) Are the events "rolling a 10" and "rolling an even number" independent? Why?

Yes, the probabilities in (a) and (b) are the same.

No, the probabilities in (a) and (b) are different.

(d) Are the events "rolling a 10" and "rolling an even number" mutually exclusive? Why?

Yes, because a number cannot be both 10 and even.

No, because if the number is 10, the number is also even.

(e) Interpret the results of parts (c) and (d).

-Dependent events are always mutually exclusive.

-Independent events are never mutually exclusive.

-Dependent events are never mutually exclusive.

-Dependent events are not necessarily mutually exclusive.

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