Answer:
P(A)=0.25
P(B)=0.077
P(AB)=0.192
P(BA)=0.083
Check below for the full numbers, I rounded it for you.
Explanation:
What is P(A), the probability that the card is a club?
So whenever you get a deck of cards you'll have 52 which have 4 suits, think of it like UNO, and club is one of the suit's name! This mean all this question is asking you is the probability of getting a club out of the 52 cards which is
52/4=13
So we know that there is 13 club cards.
Meaning the probability is a 25% since you can only get it 1/4 of the time.
P(A)=0.25
What is P(B), the probability that the card is a 5?
Same as what I stated earlier but this time you only have 4 cards that can be a "5" out of the 52 cards.
4/52=0.076923
P(B)=0.077
What is P(A and B), the probability that the card is a club and a 5?
Keep a eye on the working "and" this means it's referring to the possibility of getting a club and a 5 and since this can only happen once the chances are extremely slim.
1/52=0.1923076
P(AB)=0.192
What is P(BA), the conditional probability that the card is a 5 given that it is a club?
This assumes that you're only drawing from a deck of ONLY clubs so the chances of getting a 5 in that stack.
1/12=0.08333 (3 keeps going)
P(BA)=0.083
(This one might be wrong since I haven't done conditional probability in a long time but I feel somewhat confident, I do feel confident about the rest so no worries.)
Is P(BA) = P(B)? Are the events A and B independent?
No, P(BA) = P(B) is not true since A and B do influence one another since what if I get a 5 without replacement this results in change of chances of A.