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

an ace or a king
a king or a diamond

User Dfr
by
9.0k points

2 Answers

5 votes

a) The probability of drawing an ace or king =
(2)/(13)

b) The probability of drawing a diamond or king =
(4)/(13)

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 =
(8)/(52) [total favorable divided by the total outcome] =
(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 =
(16)/(52) [total favorable divided by the total outcome] =
(4)/(13)

Step 4 :

Answer :

a) The probability that card drawn is an ace or king =
(2)/(13)

b) The probability that card drawn is a diamond or king =
(4)/(13)

User Gaurav Ghate
by
8.6k points
2 votes

probability that the card drawn is:

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

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 = (Number-of-(ace+king)-cards)/(total-number-of-cards)


probability = (Number-of-(ace+king)-cards)/(total-number-of-cards)


probability = (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 = (Number-of-(ace+king)-cards)/(total-number-of-cards)


probability = (Number-of-(ace+king)-cards)/(total-number-of-cards)


probability = ((13+4=17))/(52)


probability = ((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
User Discodowney
by
7.3k points

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