Question

A deck consists of cards with 5 suits labelled A to E and numbered ranks from 1 to 6

. Each card is equally likely to be drawn.

Suits A

to C

are red.

Suits D

to E

are blue.

A card is drawn at random from this deck.

1) What is the probability of it having a rank less than or equal to 2 given it has a rank less than or equal to 3?

2)What is the probability that the second card is blue?

3)What is the probability that the second card is blue given that the first card is red?

4)What is the probability that the second card is blue given that the first card is blue?

5)What is the probability that the second card is blue given that the first card has rank 1?

Hint: try cases based on the color of the first card.

Answer 1

(Since there are more than 4 parts i will answer first 4)

1.

no. of ranks that are less than or equal to 3 = 3 {1,2,3}

no. of ranks that are less than or equal to 2 = 2 {1,2}

P(rank <= 2 | rank <= 3) = (no. of ranks that are less than or equal to 2) / (no. of ranks that are less than or equal to 3)

= 2/3 = 0.667

2.

P(second card blue) = P(1st card blue and second card blue) + P(1st card red and second card blue)

= (no. of blue / no. of cards)*(no. of blue remaining / no.of cards remaining) + (no. of red / no. of cards)*(no. of blue / no.of cards remaining)

= (12/30)*(11/29) + (18/30)*(12/29) = 0.4

P(second card blue) = 0.4

3.

P(second card is blue given that the first card is red) = (no. of blue) / (no, of cards remaining)

= 12/29 = 0.4138

4.

P(second card is blue given that the first card is blue) = (no. of blue remaining) / (no, of cards remaining)

= 11/29 = 0.3793

P.S. (please upvote if you find the answer satisfactory)