Question

Question #5e40c

Answer 1

1 = probability of `6/13`

2 = probability of `1/2`

3 = probability of `2/13`

Explanation:

There are 52 cards in a deck. Of them, half are red and half are black. There are always 4 of each type of card in a deck. Given this information, we can solve the three questions.

Question 1: Find the probability of getting neither a red card nor a queen. The first thing to do is eliminate half the deck, so as to get rid of the red cards. This leaves us with `1/2 * 52=26` cards.

Next, we get rid of the queens. However, two queens were already gotten rid of when all the red cards were removed, leaving only two black queens. Thus, we take two black queens away from our remaining cards, leaving us with `26-2=24` cards. The final step is to divide the 24 cards by the original 52 (`24/52`), and using simplification we arrive at the answer of `6/13`, which is the probability of getting neither a red card nor a queen.

Question 2: Find the probability of choosing a red face card. We simply get rid of all the black cards in the deck, which is `1/2` of them. This leaves us with the other `1/2` of the cards, which becomes the probability of choosing a red faced card.

Question 3: Find the probability of getting an ace or a jack. Since we know each card appears 4 times, we add together the aces and jacks to get `4+4=8` cards which we want. Then, we divide the number of aces and jacks by the total number of cards and simplify to get:

`8/52=4/26=2/13`.

Thus, the probability of getting an ace or a jack is `2/13`.