Question

what is the probability that 2 dice are the same or the sum of 8? 6 felames and 5 makes fill our for 5 job positions. how many ways can the position be filled with 3 females and 2 males? a bag of marbles contains 3 green marbles and 6 orange marbles. if you draw 2 marbles without replacemt, what are the probability of the second marble beign green?

Answer 1

1) Let X denote the event that 2 dice are the same then, there are six possible cases. While if Y denotes the number of pairs which sum up to eight is 5 which are {(2,6),(3,5),(4,4),(5,3),(6,2)}. Then the probability that 2 dice are the same or the sum of 8 is P(X or Y) =P(X) + P(Y) - P(X and Y) = 6/36 + 5/36 -1/36 = 10/36

2) The number of ways in which the positions can be filled with 3 females and 2 males is

3) There are two cases:

case 1: the first ball drawn is green: then probability than 2nd ball is green=

case 2: the first ball is orange: hen probability than 2nd ball is green=

Hence, the probability than 2nd ball is green= 1/12 + 1/4 = 1/3