A bag contains balls numbered from 1 to 42. One ball is drawn at random from these balls. The probability that its number is a multiple of 7 or 8 is:
11⁄42
Numbers from 1 to 42 that are multiples of 7: {7, 14, 21, 28, 35, 42} → 6 numbers Numbers that are multiples of 8: {8, 16, 24, 32, 40} → 5 numbers Numbers that are multiples of both 7 and 8 (LCM = 56, but 56 is not in range) → 0 numbers Using the formula for union in probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = (6/42) + (5/42) - (0/42) = 11/42
Important Questions from Probability
Three dice are thrown. What is the probability of getting a sum which is a perfect square?
Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?
Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?
Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?
What is the probability that all three boys sit together?
