Statistics -Probability or Number of Possibilities Questions

Lotto, a lottery game conducted by the Ohio State Lottery Commission, consisted of selecting six numbers from the 42 numbers 1, 2, ...,41, 42. (No repetitions are allowed, and order does not matter.) The Commission selects by chance the six winning numbers. You pay $1 to play. You get a free ticket if three of your numbers match three of the winning numbers, $75 for matching four numbers, $1500 for matching five numbers, and a large prize if you match all six numbers. The sample space consists of all possible six-number combinations that can be selected. It can be shown that n(S) = 5,245,786. The number of elements in S that match 0, 1, 2, 3, 4, 5, or 6 winning numbers is as follows:

Number of Matches Number of Possibilities
0 1,947,792
1 2,261,952
2 883,575
3 142,800
4 9,450
5 216
6 1

Please help with the following problem.
Compute the probabilities for each of the following when you throw five six-handed dice.
1) What is the probability that all five have different numbers?
2) What is the probability that at least four are the same?
3) What is the probability that exactly three are sixes?

Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete parts (a) through (e).
X 0 1 2 3 4 5 6 7 8
P(x) 0.02 0.04 0.05 0.05 0.11 0.24

Please see the attached file.
1) The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2 respectively. Let A denote the event {a, b, c} and B denote the event {c, d, e}. Determine the following:
a) P(A)
b) P(B)
c) P(A')
d) P(A U B)
e) P(A n B)
2) If the last digit

(A roulette wheel has 38 numbers: 18 red, 18 black, a 0, and a 00 (0 and 00 are neither red nor black). When the wheel is spun, all numbers are equally likely to be selected.)
What is the probability that the wheel lands on 0?
A die is loaded so that the numbers 2 through 6 are equally likely to appear, but 1 is three tim

A multi choice exam offers 4 choices for each question. Jason guesses the answers, so he has a probability 1/4 of getting any one question correct.
1) What is the expected number of right answers Jason will get if the test has 20 questions?
Data on number of puzzles solved by a person are as follows:
Puzzles solved:

Jill wants to do her MBA in Statistics at a B.C. university. She applies to two universities that offer post-graduate degrees in Statistics. Assume that the acceptance rate at University A is 25% and at University B is 35%. Further assume that acceptance at the two universities are independant events.
A) What is the probability

Let Y1<...statistics of 8 independent observations of a continuous type distribution with 70th percentile 27.3.
a) Determine P(Y7<27.3)
b) Find P(Y5<27.3