Question

A standard card deck has 52 cards consisting of 26 black and 26 red cards. Three cards are dealt from a shuffled​ deck, without replacement. Complete parts a through c below. a. Determine whether the following statement is true or false. The probability of being dealt three black cards is one half times one half times one half equals one eighth . If​ true, explain why. If​ false, show how to get the correct probability.

Answer 1

6 / 51

Explanation:

It is false.

Reason:

The probability of picking a black card at first is:

26 / 52 = 1/2

There are now 25 black cards and 51 cards in total.

The probability of picking another black card, if there's no replacement is now:

25 / 51

Now, there are 24 black cards and 50 cards left in total.

The probability of picking a black card without replacement now becomes:

24 / 50 = 12 / 25

Hence, the probability of picking three black cards without replacement is:

1/2 * 25/51 * 12 / 25 = 300 / 2550

In simplest form, it is 6 / 51