A) \[P(A)P(B)=\frac{1}{6}\]
B) A and B are independent
C) A and B are dependent
D) None of these
Correct Answer: C
Solution :
[c] When a die is thrown, the sample space (S) is \[S=\{1,2,3,4,5,6\}\] Let A: the number is even = \[\{2,4,6\}\] \[\therefore P(A)=\frac{3}{6}=\frac{1}{2}\] B: the number is red \[=\{1,2,3\}\therefore P(B)=\frac{3}{6}=\frac{1}{2}\] \[A\cap B=\{2\},P(A\cap B)=\frac{1}{6}\] or \[P(A).P(B)=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}\ne \frac{1}{6}\]
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