At Utopia University, 510 students took the College Literacy Observation Disk (CLOD) pilot test to identify any literacy traits that could be noticed.Here are the results for graduates and undergraduates.

FailPassTotal

Graduates55 125 180

Undergraduates 50 280 330

Totals105 405 510

1.For a randomly selected student, determine the following probabilities and round to 2 decimal points:

1. P(Pass) = ________
2. P(Pass and Graduate) = ________ [assume mutually exclusive (independent) events]
3. P(Fail/Undergraduate) = ________
4. P(Graduate/Fail) = ________
5. P(Pass or Undergraduate)= ________

2.Sally has 11 pairs of socks in her drawer.Each pair is a different color and design, but they are not together as pairs; they are just in her drawer scattered about. With her left hand, Sally reaches in and picks one sock.

a.While holding that one sock in her left hand, Sally reaches into the drawer and picks another sock.What is the probability of her getting a sock that will match the sock in her left hand?________ (carry to 4 decimal points)

b.Sally did not match the sock in her left hand so she discards the sock in her right hand.Still holding the initial sock in her left hand and without replacing the 1^st drawn sock (sampling without replacement and putting it aside), Sally reaches back into the drawer for another sock. What would be the probability of Sally drawing a sock on the next draw (2^nd pick) to match the initial sock she is still holding in her left hand?________ (carry to 4 decimal points)

c.Once again, Sally did not match the sock in her left hand so she discards the sock in her right hand.Still holding the initial sock and without replacing the 2^nd drawn sock (sampling without replacement and also putting it aside), Sally reaches back into the drawer for another sock. What would be the probability of Sally drawing a sock on the next draw (3^rd pick) to match the initial sock she is still holding in her left hand?________(carry to 4 decimal points)

3.Marge correctly guessed whether a fair coin turned up "heads" or "tails" on six consecutive flips.What is the probability that she will correctly guess the outcome of the next coin toss?________

4.If Johnny had 20 complete living room outfits, disregard color scheme, how many different sets of five complete outfits could be arranged?________