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!

a) 13/102

b) 24/16575

c) 169/5100

d) 30/169

Step-by-step 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

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

right

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b