A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. a) The card is a diamond, given that it is red. b) The card is red, given that it is a diamond. c) The card is a nine, given that it is red. d) The card is a king, given that it is a face card.

Step-by-step explanation:

P(A|B) = P(A and B) / P(B)

Total number of cards = 52

a)

Let A denotes the event that the card is a diamond and B denotes the card is red.

b)

Let A denotes the event that the card is red and B denotes the card is diamond.

c)

Let A denotes the event that the card is nine and B denotes the card is red.

d)

Let A denotes the event that the card is a king and B denotes the card is a face card.

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.