Question

A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades.

Four cars are drawn from the deck at random.
What is the approximate probability that exactly three of the cards are diamonds?
1%
4%
11%
44%

Answer 1

The odds are about 1%

Explanation:

In order to find this, start by determining the likelihood of drawing a diamond on the first draw.

13/52

Next subtract one from each of those numbers to get the likelihood of drawing one again (since we removed one on the first draw).

12/51

Next do this a third time, subtracting one from both numbers.

11/50

Finally, use the opposite for the last draw since we want it to not be a diamond.

39/49

Now, to get the probability, multiply them all together.

13/52 * 12/51 * 11/50 * 39/49 = .01 = 1%

Answer 2

Answer: a) 1%

Explanation:

1st draw and 2nd draw and 3rd draw and 4th draw

`(13)/(52)` x
`(12)/(51)` x
`(11)/(50)` x
`(39)/(49)` =
`(66,924)/(6,497,400)`

= 0.01

= 1%