1. A small delegation of k students is chosen by lot (at random) from a class of size n to complain about a certain aspect of the course . Assume Flora and Mike are in the class and that 1
a. Is the probability that Mike is in the delegation 1/k, 1/n, or something else?
b. What is the probability that Flora is in the delegation?
c. Are the events "Mike is in" and "Flora is in "independent?
2. A die is weighted so that
a 3 comes up 7 times as often as 4
b 4 comes up twice as often as 1, 2, 5. And 6
c 1, 2, 5, and 6 are equally likely
Let X denote that outcome of any roll and let q=P(X=4).
Part1: Determine the probability distribution for X and the value for q
Part2: Find E(X), the expected value of X.
3. A bank "password" is a sequence of 4 digits. If passwords were generated at random, what would be the expected number of 5's?
4. It is known that 85% of individuals who purchase a make of laptop do not make any claims on their guarantee. Suppose 43 customers buy that make of laptop. Computer the probability that at least three owners will make a claim on their guarantee.
5. Suppose that in a certain board game player A will win if she rolls a 4 on either or both of two unbiased dice.
AWhat is the probability that she will win on her next roll?
B How many rolls should she expect to roll until she wins?
6. Imagine a gambling game played with an ordinary deck of 52 cards. You pay $2.5 to play and you play by shuffling the deck and then turning over the top card
- If the top card is a diamond, you win $4.5
- If the top card is a picture (face) car, you win $4.5, but J, Q or K of diamonds wins $7.00
- If the top card is an ace, you win $5.00, but the ace of diamonds win $10.00
- If the top card is a any other card, you win nothing
Q1: let f be your payoff, that is your win minus the $2.5, then f has a value for every card turned up, but only has 5 different values. Determine the probability distribution for these values.
Q2: Calculate the expected value for f.
Q3 Why is the average payoff per play negative?