Answer:
13/102
8/5525
169/5100
10/39
Step-by-step explanation:
a. there are 26 red cards in a standard deck and 13 clubs
P (red) = 26/52 =1/2
Then we keep the card, so there are only 51 cards left
P ( club) = 13/51
P (red, no replacement, club) = P (red) * P(club) = 1/2 *13/51 = 13/102
b. there are 4 three's in a standard deck 4 7's 12 face cards, assuming an A is not a face card (jack , queen king are face cards, 1 of each suit 3*4 =12)
P (3) = 4/52 =1/13
Then we keep the card, so there are only 51 cards left
P (7) = 4/51
Then we keep the card, so there are only 50 cards left
P (face card) = 12/50 = 6/25
P (3, no replacement, 7,no replacement, face)
= P (3) * P(7)* P (face) = 1/13 *4/51*6/25 =8/5525
c. there are 13 diamonds in a standard deck 13 hearts and 26 black cards
P (diamond) = 13/52 =1/4
Then we keep the card, so there are only 51 cards left
P (heart) = 13/51
Then we keep the card, so there are only 50 cards left
P (black) = 26/50 = 13/25
P (diamond, no replace, heart,no replace, black)
= P (diamond) * P(heart)* P (black) = 1/4*13/51*13/25 =169/5100
d assuming an aces is a number card
there are 40 number cards and 12 face cards
P (number) = 40/52 =10/13
Then we keep replace card, so there are 52 cards left
P ( face) = 12/52=1/3
P (number, replace, face) = 10/13 * 1/3 =10/39
