Question

(Note that an Ace is considered a face card for this problem)
In drawing a single card from a regular deck of 52 cards we have:

(a) P( black and a face card ) =
(b) P( black or a face card ) =
(c) P( black or a 3 ) =
(d) P( Queen and a 3 ) =
(e) P( black and a Queen ) =

Answer 1

A card is drawn at random from a standard deck of 52 cards.

Now there are 26 black cards; 4 face cards (king queen, jack, ace) and 9 number cards of each denomination.

No. of denominations =4.

Let A denote a black card, B denote a face card, C denote a face card of queen and D denote a number card of 3.

a) No. of face cards which are black =8.

b) Total no.of a face cards = 4*4=16.

since there are 4 face cards of each denominations.

Total no. of black cards= 26.

  

c) No of black cards = 26.

No. of cards numbered 3 = 4.

No. of black cards which are numbered 3 = 2

  

d) No. of cards which are queen = 4.

No. cards which are numbered 3 = 4.

There are no cards which are both queen and 3.

Therefore no. of cards which are both queen and 3 =0.

e) No. of cards which are black as well as queen = 2.