In a box there are 3 red and 5 blue cards. These cards are numbered 1-3 for red and 1-5 for blue. Let the event B: blue cards drawn, E: even number of card is drawn. Obtain P(E/B)

Answer 1

Naively, the even blue cards are 2 and 4 . So 2/8 = 1/4 = 0.25 = 25%

There's 5/8 change of getting the blue card, and from that 2/5 that is it even.

The product is 5/8*2/5 = 2/8 = 1/4 = 0.25 = 25%

Answer 2

Use the conditional probability formula which in this case is:

Pr ( E Ι B ) = Pr ( E ∩ B ) / Pr ( B )

Pr ( E ∩ B ) =2/8 two of the 5 blue cards are even numbered of the total of 8 cards

Pr ( B ) = 5/8 five of the 8 cards are blue

So Pr ( E Ι B ) = (2/8) / (5/8) = 2/5