Question

Given a standard deck of cards, find the following:
a) ?(7 of spades | black card)
b) The probability that the first card is red and the second is the King of Clubs (this is a black card)
c) The probability that the first card is the King of Clubs and the second is red
d) What is the probability of drawing 3 kings when drawing 3 cards?

Answer 1

a. Th​​​​e probability of p(7 of spades / black card)

Ans : The deck of cards divided into 4

They are spades-13

hearts-13

Diamonds-13

Clubs-13

The probability of drawing the seven of spades from a deck of cards is (black)

P(A) = 1/52

b. The probability that the first card is red and the second is the king of clubs(black card)

Ans: The probability that the first card red is p(A) = 26/52

  p(A) = 1/2

The probability that the second is the king of clubs that is black

p(B) = 1/52

Then the probability that the first card is red and the second is the king of clubs are =(1/2)(1/52)

c.The probability that the first card is king of clubs and the second is red

Ans: The probability that the first card king of clubs is p(A) = 1/52

The probability that the second card red is p(B) = 1/2

Then the probability of first card king of clubs and The second card red is = (1/52) (1/2)

d. What is the probability of drawing 3 Kings when drawing 3 cards

Ans : There are 52 possible cards for first draw

Only 51 for the second draw

And for 50 for the third draw

=52*51*50

= 132,600 possible

If we drew only Kings the first card drawn 4,next 3, and next 2

= 4*3*2 = 24

So the probability of draw 3 Kings at random from a deck of 52 cards is

= 24/132,600

= 1/5,525

~ 0.01181%