Question

A card is drawn at random from a deck of 52 playing cards. Find the probability that the card drawn is:

Answer 1

probability that the card drawn is:

1. an ace or a king  = 0.1538
2. a king or a diamond = 0.3269

Step-by-step explanation:

Here we have , A card is drawn at random from a deck of 52 playing cards. We need to find that Find the probability that the card drawn is:

• an ace or a king

A deck of standard 52 cards contain four aces. There are four kings in a standard deck of playing cards. So ,we need to find probability that card drawn is either a ace or king i.e.

$probability = \frac{Number-of-(ace+king)-cards}{total-number-of-cards}$

⇒ $probability = \frac{Number-of-(ace+king)-cards}{total-number-of-cards}$

⇒ $probability = \frac{8}{52}$

⇒ $probability = 0.1538$

• a king or a diamond

A deck of standard 52 cards contain four kings. There are 13 Diamonds in a standard deck of playing cards. So ,we need to find probability that card drawn is either a ace or king i.e.

$probability = \frac{Number-of-(ace+king)-cards}{total-number-of-cards}$

⇒ $probability = \frac{Number-of-(ace+king)-cards}{total-number-of-cards}$

⇒ $probability = \frac{(13+4=17)}{52}$

⇒ $probability = \frac{(17)}{52}$

⇒ $probability =0.3269$

Therefore, probability that the card drawn is:

1. an ace or a king  = 0.1538
2. a king or a diamond = 0.3269

Answer 2

a) The probability of drawing an ace or king =  $\frac{2}{13}$

b) The probability of drawing a diamond or king =  $\frac{4}{13}$

Step-by-step explanation:

Step 1 :

Total number of cards in the deck = 52

We need to compute probability that card drawn is

a) ace or king

b) King or diamond

Step 2 :

a)

Number of ace in the pack = 4

Number of kings in the pack = 4

Hence the probability of selecting an ace or king =  $\frac{8}{52}$ [total favorable divided by the total outcome] = $\frac{2}{13}$

Step 3:

b)

Number of king in the card deck = 4

Number of diamond in the card deck = 13

Number of diamond cards which is a king = 1

Total number of cards that can be drawn ( king or diamond) = 4 + 13 - 1 = 16

Hence probability that a diamond or king is drawn =  $\frac{16}{52}$  [total favorable divided by the total outcome]  =  $\frac{4}{13}$

Step 4 :

Answer :

a) The probability that card drawn is an ace or king =  $\frac{2}{13}$

b) The probability that card drawn is a diamond or king =  $\frac{4}{13}$