SOLUTION: suppose that all possible card selections are equally likely, what probability should be assigned to each selection? Find the probability that you choose a face card.(j,q,k,a) Fi

Question 854669: suppose that all possible card selections are equally likely, what probability should be assigned to each selection?
Find the probability that you choose a face card.(j,q,k,a)
Find the probability that you choose a black card, spade or club.
consider the events" draw a face card and draw a 5 or smaller'. Are these events overlapping or disjoint? explain
Find the probability of drawing a red card or a spade.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
52 cards in the deck.

face card is any card with a face on it.
that would be jack, queen, king.
ace is not considered a face card.
there are 4 jacks, 4 queens, 4 kings in the deck for a total of 12.
probability of getting a face card is 12 / 52 which is equivalent to 3 / 13.

there are 26 black cards in the deck (spades and clubs) and 26 red cards in the deck (hearts and diamonds).
the probability of getting a black card only is therefore equal to 26/52 = 1/2.
since a spade or a club are both black cards, the probability remains the same.
this is the probability of A or B or C.
A is the probability of getting a black card.
B is the probability of getting a spade.
C is the probability of getting a club.

the formula for the probability of (A or B or C) is equal to the p(A) + p(B) + p(C) - p(AB) - p(AC) - p(BC) + p(ABC).
p(A) = 26/52
p(B) = 13/52
p(C) = 13/52
p(AB) = 13/52
p(AC) = 13/52
p(BC) = 0
p(ABC) = 0
put those numbers in the formula and you get 26/52 as the answer.
p(AB) is 13/52 because there are 13 spades in the deck and they are all black.
p(AC) is 13/52 because there are 13 clubs in the deck and they are all black.
p(BC) is 0 because the same card can't be a spade and a club at the same time.
p(ABC) = 0 because the saem card can't be a spade and a club and a black card at the same time.

the event of drawing a face card and drawing a 5 or smaller are disjoint event.
this is because you can't draw a face card and a 5 or smaller at the same time.
this is because none of the number cards are face cards and so there is no overlap.

an example of an overlap would be drawing a spade and drawing a 5 or smaller. in this case, there are overlapping events because a 5 or smaller could also be a spade.

the probability of drawing a red card or a spade is equal to 26/52 + 13/52.
this is because red cards and spades are disjoint event. they have nothing in common.

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