Question

From a standard deck of cards, what is the probability of choosing...

a) a red and then a club without replacement?
b) a 3, then a 7, then a face card without replacement?
c) a diamond, then a heart, then a black card without replacement?
d) a number card then a face card with replacement?

You have to answer a,b,c, and d to get the full amount of 50 points!!! good luck!

Answer 1

a) 13/102

b) 24/16575

c) 169/5100

d) 30/169

Explanation:

a) 26/52 × 13/51

13/102

b) 4/52 × 4/51 × 12/50

1/13 × 4/51 × 6/25

24/16575

c) 13/52 × 13/51 × 26/50

1/4 × 13/51 × 13/25

169/5100

d) 40/52 × 12/52

10/13 × 3/13

30/169

Answer 2

13/102

8/5525

169/5100

10/39

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