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
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 boys and girls sit alternatively?
What is the probability that P and Q take the two end positions?
