Question

a card is drawn at random from a deck of cards. find the probability that the card drawn is
1)a king or a jack
2)non-ace
3)a red card
4)neither a king nor a queen

Answer 1

You did not specify if it’s a 32 or 52 cards deck.

Let say you meant a 52 cards deck.

There is 2 red aces in the deck
There is 12 heart in the deck (I skipped the heart ace already in the first set)
Thus there is 14 matching cards out of 52.

Thereforce the probability is 14/52 ie 7/26

Answer 2

Total number of cards in a deck n(S) = 52.

(1)

Let E₁ be the event of drawing a king or a jack.

We know that there are 4 jacks and 4 kings = 4 + 4 = 8

Favorable outcomes n(E₁) = 8

∴ Required probability P(E₁) = n(E₁)/n(S)

⇒ 8/52.

(2)

Let E₂ be the event of drawing a non-ace card.

We know that there are 4 ace cards.

n(E₂) = 4.

Non-ace cards n(E₂) = 52 - 4 = 48.

∴ Required probability P(E₂) = n(E₂)/n(S)

⇒ 48/52.

(3)

Let E₃ be the event of getting a red card.

We know that total number of red cards n(E₃) = 26.

Required probability P(E₃) = n(E₃)/n(S)

⇒ 26/52

⇒ 1/2.

(4)

Let E₄ be the event of drawing neither a king nor a queen.

Total number of kings + queens = 8.

Neither a king or queen = 52 - 8

                                         = 44.

Required probability P(E₄) = n(E₄)/n(S)

⇒ 44/52.

Hope it helps!