Mth212 Probability (Part 2)

[K] Bag#1 has 1 Black and 3 White marbles in it; Bag#2 has 2 Black and 2 White marbles in it. The experiment is as follows: First you reach into Bag#1, choose a marble, and place it into Bag#2. Then, you reach into Bag#2 and draw out a marble. What is:

i) P(2nd Draw is Black if you know that 1st Draw is White) ii) P(2nd Draw is Black if you know that 1st Draw is Black) iii) P(2nd Draw is Black) iv) P(2nd Draw is White)

[L] There are 7 lottery tickets, but only 4 winning tickets. You select a ticket randomly. What are the odds of winning?

[M] At a carnival game, you have a 10% chance of winning 10.00 $, a 30% chance of winning 5.00 $, and a 60% of winning 1.00$.

i) What is the expected value for this game? ii) If the game costs 4.00 $ to play, then what is the expected average loss ?

[N] There are some ID Cards made at EWU that consist of 6 letters and 3 digits, but no repetition of letters or digits is allowed. What it the probability that I get an ID card containing the letters “D” “A” “N” “I” “E” “L”

i) In exactly that order? ii) In any order ?

[O] Consider a string of letters to mean just an ordered list of letters: For example, “QRST” and “SQRT” are two different strings containing the same letters.

How many different 8-letter strings can be made from the letters in the word “EQUATION” if:

i) There are no restrictions? ii) The first letter must be a consonant? iii) The last letter must be a vowel? iv) The first letter must be a consonant and the last letter must be a vowel?

[P] A school dance committee of 5 people is selected at random from a group of 8 ninth graders, 10 eighth graders, and 9 seventh graders.

i) What is the probability that the committee has all eighth graders? ii) What is the probability that the committee has no ninth graders? [Q] Eight club members decide to choose officers at random. They need a President, Vice President, and Treasurer.

i) How many ways are there to do this? ii) What is the probability that club member Heidi is chosen to be an officer?

[R] There are 6 identical Math books and 12 identical English books.

i) How many different ways can these books be lined up on the shelf? ii) How many different ways can they be lined up if the first book must be an English book?

[S] You’ll be dealt seven cards from a standard deck. What is the probability:

i) You get 4 Aces and 3 Queens? ii) You get all Spades? iii) You have a 2, 3, 4, 5, 6, 7, 8 ? ------

SuperSox

Drawer has 7 Socks: (3 Red, 2 Blue, 2 Green) You reach in & randomly grab two socks. i) P(The socks are both Red) ii) P(The socks are same color) iii) P(At least one sock is Blue) iv) P(Neither sock is Green)

Special [K]

3 White 5 White 4 Black 2 Black

Bag1 Bag2

Step1: Pick Ball Bag2 from Bag1 Put Into

Step2: Pick Ball from Bag2

** What is P(You End up w/ White?) **