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2.1. There are 40 pairs of shoes in Bill’s closet. They are all mixed up. If 20 shoes are picked, what is the chance that all 20 are from a unique pair, in other words you have no pairs of shoes? Please round to 2 decimals.2.

2.2. A chessboard is an eight-by-eight arrangement of 64 squares. Suppose eight

chess pieces are placed on a chessboard at random so that each square can

receive at most one piece. What is the probability that there will be exactly

one piece in each row and in each column? Round to 6 decimals.

I got partial credit on the next following questions, not sure which ones are wrong! My answers are bolded.

3.1 10/15 points: Suppose you throw five dice and all outcomes are equally likely.

(a) What is the probability that all dice are the same? (In the game of Yahtzee,

this is known as a yahtzee.) 0.00077 Round to 5 decimal places

(b) What is the probability of getting at least one 4? 0.598 Round to 3 decimal places

(c) What is the probability that all the dice are different? 0.0926 Round to 4 decimal places

3.3 18/24 (2 are wrong) The diagram for this is attached. Find the following: (type the letter with a + if multiple letters are needed)

(a) P(No events occur). h

(b) P(Exactly one event occurs). a+c+f

(c) P(Exactly two events occur). b+d+e

(d) P(Exactly three events occur). g

(e) P(At least one event occurs). a+b+c+d+e+f+g

(f) P(At least two events occur).put letter in alphabetical order b+d+e+g

(g) P(At most one event occurs).put letter in alphabetical order a+c+f+h

(h) P(At most two events occur). a+b+c+d+e+f+h

There are three more questions I need help with that are attached. 1.41, 1.43 and 1.44.

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