A pair of dice is rolled once. (a) Find the probability of rolling a 10. (Enter

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). Independent events are never mutually exclusive. Dependent events are never mutually exclusive. Dependent events are always mutually exclusive. Dependent events are not necessarily mutually exclusive

Explanation / Answer

a) probability of rolling a 10 =(3/36)=1/12 (as out of 36 outcome 3 comes 10 as sum)

b)probability of rolling a 10 given that the number rolled is even =P(sum is 10 given sum is 2; 4;6;8;10;12)

=3/(1+3+5+5+3+1) =3/18=1/6

c)

no the probabilities in (a) and (b) are different

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

e)

Dependent events are not necessarily mutually exclusive

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