Q. 7. The probability that a student passes statistics is 2/3, and the probability that he passes mathematics is 4/9. If the probability of passing both the courses is 1/4, what is the probability that the student passes at least one of these courses? (Jan. 2001, Dec. 2000)

Solution.
Let A = (the event that the student passes statistics)
B = (the event that the student passes mathematics)
Given, P(A) = 2/3, P(B) = 4/9, P(A Ç B) = 1/4
(A È B) = The event that the student passes at least one of the courses
P(A È B) = 2/3 + 4/9 - 1/4 = 31/39
Hence, the required probability is 31/39.

Q. 8. If the probabilities that a person purchasing a new car will choose green, white, red or blue colour are 0.08, 0.09, 0.15 and 0.21 respectively, then what is the probability that a given buyer will choose a new car which has any one of these colours? (June 2001)

Solution. Here the event of buying a car of particular colour is mutually exclusive, i.e., the buyer will purchase either a car of any of the four colours.
Let A = an event that the buyer selects a green car
B = an event that the buyer selects a white car
C = an event that the buyer selects a red car
D = an event that the buyer selects a blue car
Therefore, P(A È B È C È D) = P(A) + P(B) + P(C) + P(D)
or P(A È B È C È D) = 0.08 + 0.09 + 0.15 + 0.21 = 0.53
Hence, the required probability is 0.53.