The question is incomplete. Here is the complete question.
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.
What is P(A), the probabillity that the six-sided die is an even number?
What is P(B), the probability of the four-sided die is an odd number?
What is P(A and B), the probability that the six-sided die is an even number and the four-sided die is an odd number?
Are events A and B independent?
a) Yes, events A and B are independent events.
b) No, events A and B are not independent events.
Answer: P(A) = 1/2
P(B) = 1/2
P(A and B) = 1/4
a) Yes, events A and B are independent events.
Step-by-step explanation: The event A is related to a six-sided die, so total possibilities is 6.
For a six-sided die to show a even number, there are 3 possibilities: (2,4,6)
so, P(A) = 3/6 = 1/2
The event B is for a 4-sided die, i.e. total possibilities is 4.
To show an odd number, there are 2 possibilities: (1,3).
Then, P(B) = 2/4 = 1/2
Now, the probability of occuring A and B is:
P(A and B) = P(A).P(B)
P(A and B) = 1/2*1/2
P(A and B) = 1/4
The events are independent events because the probability of A happening does not influence the occuring of event B.