Assertion (A): If A and B are independent events, then A' and B' are also independent. Reason (R): P(A'∩B') = P(A')P(B') when A and B are independent. Choose the correct option:
A.A is true, R is false
B.Both A and R are true, but R is not the correct explanation of A
C.A is false, R is true
D.Both A and R are true, and R is the correct explanation of A
Explanation:
If A and B are independent, then their complements are independent. The formula P(A'∩B') = (1-P(A))(1-P(B)) holds, so R is true and explains A.
Explanation:
The sample space lists all possible elementary outcomes; for a standard six-sided die, these are the integers 1 through 6, each equally likely in a fair roll.
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