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
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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 theevents "rolling a 10" and "rolling an even number" independent? Why?
(d) Are the events "rolling a 10" and "rolling an even number" mutually exclusive? Why?
(e) Interpret the results of parts (c) and (d).
(b) Find the probability of rolling a 10 given that the number rolled is even. (Enter your answer as a fraction.)
(c) Are the
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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