Question

You are given 40 cards with four different colors- 10 Green cards, 10 Red Cards, 10 Blue cards, and 10 Yellow cards. The cards of each color are numbered from one to ten. Two cards are picked at random. Find out the probability that the cards picked are not of the same number and same color.

Answer 1

Since these events are not independent, we can use the rule:

P(A and B) = P(A) * P(B|A) ,which is also equal to

P(not A and not B) = P(not A) * P(not B | not A)

For example:

P(not 4 and not yellow) = P(not 4) * P(not yellow | not 4)

P(not 4 and not yellow) = (36/39) * (27/36)

P(not 4 and not yellow) = 0.692

Therefore, the probability that the cards picked are not the same number and the same color is 69.2%.