Engineering Board Exam Reviewer · Mutually Exclusive and Independent Events · medium
Two fair dice are rolled. Let A be the event that the sum is 8 and B the event that the first die shows 4. Are A and B independent?
- Yes, because P(A B)=P(A)P(B)
- No, because P(A B)= 136 P(A)P(B)= 5216
- Yes, because the dice are fair
- No, because A and B are mutually exclusive
Answer
B. No, because P(A B)= 136 P(A)P(B)= 5216
Solution
P(A)= 536, P(B)= 16, and A B=(4,4) so P(A B)= 136. Since P(A)P(B)= 5216 136, the events are not independent. (They are not mutually exclusive either, since (4,4) is in both.)
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