( a ) Assuming the card selection is with replacement .
( b ) Assuming the card selection is without replacement .
6 . There are 2000 students in a high school . Among the 2000 students , 1500 students have a laptop , and 900 students have a tablet . 500 students have a laptop and a tablet . Let L be the event that a randomly selected student has a laptop , and T be the event that a randomly selected student has a tablet . ( Show all work . Just the answer , without supporting work , will receive no credit .)
( a ) Provide a written description of the complement event of ( L OR T ).
( b ) What is the probability of complement event of ( L OR T )?
7 . Consider rolling a fair 6-faced die twice . Let A be the event that the sum of the two rolls is at most 6 , and B be the event that the first one is an even number .
( a ) What is the probability that the sum of the two rolls is at most 6 given that the first one is an even number ? Show all work . Just the answer , without supporting work , will receive no credit .
( b ) Are event A and event B independent ? Explain .
8 . Answer the following two questions . ( Show all work . Just the answer , without supporting work , will receive no credit ).
( a ) The steering committee of UMUC Green Solutions Team consists of 3 committee members . 10 people are interested in serving in the committee . How many different ways can the committee be selected ?
( b ) A bike courier needs to make deliveries at 6 different locations . How many different routes can he take ?