Probability Question 291
Question: A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, “the number is even”, and B be the event, “the number is red” then;
Options:
A) $ P(A)P(B)=\frac{1}{6} $
B) A and B are independent
C) A and B are dependent
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
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} $
BETA
