Two cards are drawn without replacement from a deck of 52 cards.
Determine P(A and B) where
A : the first card is a spade
B: the second card is a face card
please help!!
Since a tutor hasn't answer I'll try
A. 1st is a spade
P = S/N
Number of spades in deck = 13 = S
Number of cards = 52 = N
P = S/N = 13/52 = 1/4
B. 2nd is a face card
P = S/N
Number of face cards in deck = 13 = S
Number of cards = 52 - 1 = 51 = N
P = S/N = 13/51
P = P(A) * P(B)
P = 1/4 * 13/51 = 13/204
Not a tutor but I think it is correct
maybe a tutor will answer
number of spades = 13
number of face cards = 12
number of face OR faces = 21
P(A and B) = P(A) + P(b) - P(A or B)
= 13/52 + 12/52 - 21/52 = 4/52 = 1/13
Number of Spades in deck=1/13
To determine P(A and B), you need to find the probability that the first card is a spade (event A) and the second card is a face card (event B).
First, let's find the probability of event A occurring. There are 52 cards in a standard deck, and 13 of them are spades. Therefore, the probability of drawing a spade as the first card is 13/52.
Next, let's find the probability of event B occurring. After one card is drawn, there are 51 cards remaining in the deck, and 12 of them are face cards (since we already removed one card which is a spade). Therefore, the probability of drawing a face card as the second card is 12/51.
We are drawing the cards without replacement, which means the first card is not being put back into the deck before drawing the second card. As a result, the number of cards available for the second draw decreases by one.
To find the probability of both events A and B occurring, we multiply the probabilities of each event together: P(A and B) = P(A) * P(B)
P(A and B) = (13/52) * (12/51)
Simplifying this fraction gives:
P(A and B) = (1/4) * (4/17)
P(A and B) = 1/17
Therefore, the probability of drawing a spade as the first card and a face card as the second card, without replacement, is 1/17.