Three cards are drawn from a deck of 52 playing cards and not replaced. Find the probability of the following:

Question

a) Getting three jacks
b) Getting an ace, a king, and a queen in order.
c) Getting a club, a spade, and a heart in order
d) Getting three clubs

Answer 1

OK, for the first one, the chances of the first one being a Jack are 4/52. The chances for the second one are 3/51, and the chances for the third are 2/50. Multiply them together and you get 24/52*51*50, or 1/5525.

For the second, the odds for the first card being an ace are 4/52. The odds of the second one being a king are 4/51, and the odds of the third being a queen are 4/50. So the odds are 64/52*51*50, or 8/16575, or 1/2071.875.

The third question works just like the second one, except there are 13 cards per suit, rather than 4. So the odds for the first card are 13/52, 13/51 for the second and 13/50 for the third. Total odds: 13^3/52*51*50, or 169/10200, or 1/60.355.

The last question works similarly to the first. The odds of the first card being a club are 13/52. The odds for the second are 12/51, and for the third 11/50. Overall odds: 13*12*11/52851*50, or 11/850, or 1/77.(27)repeating.

Answer 2

I'm not really into doing peoples HW for them but this too easy.
a) 4/52 x 3/51 x 2/50 = calculate
b) 4/52 x 4/51 x 4/50 = idk, you'll have to calculate it.
you always times if its an "and" but you add if its an "or"
c)13/52 x 13/51 x 13/50= calculate
d) 13/52 x 12/51 x 11/50= calculate
the club number goes down b/c your not replacing it. You have 13 clubs, you take one out, now you have 12 and 51 cards in all.

I don't feel too bad doing this because you still need to so most of the math. This is too easy hun!

Answer 3

4 jacks: 4/52 * 3/51 * 2/50 = 1/5525 4 aces, kings, queens: 4/52 * 4/51 * 4/50 = 8/16575 13 clubs, 13 spades, 13 hearts: 13/52 * 13/51 * 13/50 = 169/10200 13 clubs: 13/52 * 12/51 * 11/50 = 11/850 Hope this helps! :)

Answer 4

a) Getting three jacks 4/52*3/51*2/51
b) Getting an ace, a king, and a queen in order. 4/52*4/51*4/50
c) Getting a club, a spade, and a heart in order13/52*13/51*13/50
d) Getting three clubs 13/52*12/51*11/50

Answer 5

Hey, that's four questions! That should be eight points :)

Three jacks would be 1/13 x 1/17 x 1/25

AKQ would be 1/13 x 4/51 x 2/25

CSH would be 1/4 x 13/51 x 13/50

Three clubs would be 1/4 x 4/17 x 11/50

Answer 6

a) = 4/52 * 3/51 * 2/50 = 24 / 132,600 = 3/16575 = 1/5,525

b)4/52 * 4/51 * 4/50 = 64 / 132,600 = 16/33,150

c) 13/52 * 13/51* 13/50 = 2,197/132,600

d) 13/52*12/51*11/50 = 1,716/132,600

Answer 7

a, 4/52 x 3/51 x 2/50
b, 4/52 x 4/51 x 4/50
c, 13/52 x 13/51 x 12/50
d, 13/52 x 12/51 x 11/50

Answer 8

49 duh