Answer:
Option B is correct
Step-by-step explanation:
Given the rolling a fair six-sided die once.
The probability of the event A "rolling a 5" is P(A) = 1/6
(There is only a number 5 out of 6 numbers of a die)
The probability of the event B "rolling an odd number" is P(B) = 3/6
(There are 3 odd numbers out of 6 numbers of a die including 1, 3, and 5)
The probability of the event that is "rolling a 5" and "rolling an odd number" is P(A⋂B) = 1/6
(There is only a number satisfying the above event, that is number 5)
If the two events A and B are independent, we will have:
P(A) x P(B) = P(A⋂B)
Now, we check:
(1/6) x (3/6) = (1/6) <=> 1/12 = 1/6 (invalid)
=> A and B are not independent
=> A and B are dependent => Option C and D are incorrect
As the correct formula of conditional probability in case that two events are independent (P(A) = P(A|B) or P(B) = P(B|A)) => Option A is incorrect
=> Only option B is correct
I hope this helps!
