Question

A card is drawn at random from a pack of 52 cards . Find the probability of that card drawn is a). a black queen, b). a jack ,a queen , a king. c). a card of diamond ,d). a red card, e). a jack.

Answer 1

a. 2 ÷ 52
b. 12 ÷ 52
c. 13 ÷ 52
d. 26 ÷ 52
e. 4 ÷ 52

Answer 2

A card can be drawn out of 52 cards in 52 ways.
the sample space S contains 52 sample points.
n (S)=52
a)Let A be the event that the card drawn is a black queen.
There are 2 black queens. (1 club and 1 spade)
n (A)=2
P(A)=n(A)/n (S)=2/52=1/26
b)Let B be the event that the card drawn is a king.
There are 4 kings. (2 red and 2 black)
n (B)=4
P (B)=n (B)/n(S)=4/52=1/13
Let C be the event that the card drawn is a queen.
There are 4 queens. (2 red and 2 black)
n (C)=4
P (C)=n (C)/n(S)=4/52=1/13
c) Let C be the event that the card drawn is a card of diamond.
There are 13 diamond cards.
n (D)=13
P(B)=13/52
d)Let E be the event that card drawn is a red card.
There are 26 red cards.( 13 heart and 13 diamond)
n (E)=26
P(E)=n (E)/n (S)=26/52=1/2
e)Let F be the event that the card drawn is a jack.
There are 4 jack cards.
n (F)=4
P (F)=n (F)/n(S)=4/52=1/13.
Hope it helps.