Find the probability for the experiment of drawing a card at random from a standard deck of 52 playing cards.

1. The card is a face card.

2. The card is not a face card.

3. The card is a red face card.

4. The card is a 6 or lower. (Aces are low.)

5. The card is a 9 or lower. (Aces are low.)

1. 12/52 or 0.2308

2. 10/13 or 0.7692

3. 3/26 or 0.1154

4. 3/26 or 0.1154

5. 9/52 or 0.1731

Step-by-step explanation:

1.

The face card are king, queen and jack.

There are 12 face card in a deck of 52 cards i. e. 4 king, 4 queen and 4 jack.

P (FC) = 12/52 or 0.2308

So, the probability that the card is a face card is 0.2308.

2.

The card is not a face card.

P (FC') = 1-P (FC) = 1 - (12/52) = (52-12) / 52=40/52=10/13

P (FC') = 10/13 or 0.7692

So, the probability that the card is not a face card is 0.7692.

3.

The card is a red face card

There are 6 red face card in a deck of 52 cards i. e. 2 king, 2 queen and 2 jack.

P (RFC) = 6/52

P (RFC) = 3/26 or 0.1154

So, the probability that the card is a red face card is 0.1154.

4.

The card is a 6 or lower.

There are 6 cards in a deck of 52 cards that are 6 or lower i. e. 6,5,4,3,2 and ace.

P (6 or lower) = 6/52

P (6 or lower) = 3/26 or 0.1154

So, the probability that the card is a 6 or lower is 0.1154.

5.

The card is a 9 or lower.

There are 9 cards in a deck of 52 cards that are 9 or lower i. e. 9, 8, 7, 6, 5, 4, 3, 2 and ace.

P (9 or lower) = 9/52

P (9 or lower) = 9/52 or 0.1731

So, the probability that the card is a 9 or lower is 0.1731.