1. A basket contains 1 white balls, 5 yellow balls, and 4 red balls. Consider selecting one ball at a time from the basket. ( Show all work. Just the answer, without supporting work, will receive no credit. )

(a) Assuming the ball selection is with out replacement . What is the probability that the first ball is w h i t e and the second ball is r e d ?

(b) Assuming the ball selection is with replacement . What is the probability that the first ball is r e d and the second ball is also r e d ?

2. There are 1 0 00 juniors in a college. Among the 1 0 00 juniors, 4 00 students are taking STAT200, and 7 0 0 students are taking PSYC300. There are 2 0 0 students taking both courses. Let S be the event that a randomly selected student takes STAT200 , and P be the event that a randomly selected student takes PSYC300 . ( Show all work. Just the answer, without supporting work, will receive no credit. )

(a) Provide a written description of the complement event of ( S OR P ) .

(b) What is the probability of complement event of ( S OR P ) ?  

 3. Consider rolling a fair 6 - faced die twice. Let A be the event that the sum of the two rolls is equal to 7 , and B be the event that the first one is a n odd number .

(a) What is the probability that the sum of the two rolls is equal to 7 given that the first one is an odd number ? Show all work. Just the answer, without supporting work, will receive no credit .

(b) Are event A and event B independent? Explain.

4. Answer the following two questions . ( Show all work. Just the answer, without supporting work, will receive no credit ) .

(a) UMUC Stat Club is sending a delegate of 2 members to attend the 201 8 Joint Statistical Meeting in Vancouver . There are 10 qualified candidates. How many different ways can the delegate be selected?

(b) A bike courier needs to make deliveries at 5 diffe rent locations. How many different routes can he take?  

5. Mimi joined UMUC basketball team in spring 201 7 . On average, she is able to score 2 0% of the field goals. Assume she tries 1 0 field goals in a game.

(a) Let X be the number of field goals that Mimi scores in the game. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that Mimi scores at least 3 of the 1 0 field goals. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.