Question

41 different balls are drawn from a bag containing balls labelled 1,2,…,300. The probability that the number of balls drawn that are labelled with an odd number is larger than the number of balls drawn that are labelled with an even number can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?

Answer 1

There are 150 odd balls and 150 even balls, the probability is the sum over the probabilities to draw k balls for k = 21 to 41. The equal number of even and odd balls implies that the probability that the number of even balls is larger is the same. Because there is no draw possible, both probabilities are 1/2.

Answer 2

an urn contains 6 balls identical in every aspect except color. theres is one yellow ball 2 red balls and 3 blue balls. you draw two balls from the urn but replace the first ball before drawing the second. find the probability that the first ball is blue and the second is red