Question

1.To win the Michigan Lotto a person must correctly pick 6 distinct numbers from the numbers 1 through 46. A lotto ticket cost $1. If you buy 1000 tickets (and choose different sets of six numbers for each tickets, of course), What is the probability that you will have the winning set numbers?

2.Salespersons Adams and Jones call on three and four customers, respectively, on a given day. Adams could make 0, 1, 2, or 3 sales, whereas Jones could make 0, 1, 2, or 3 sales. The sample space listing the number of possible sales for person on a given day is given in the following table. Here (0, 1) stands for 0 sales by Adams and 1 sale by Jones. Assume that each sample point is equally likely.

Adams	Jones 0------1------2------3
0	{0, 0} {1, 0} {2, 0} {3, 0}
1	{0, 1} {1, 1} {2, 1} {3, 1}
2	{0, 2} {1, 2} {2, 2} {3, 2}
3	{0, 3} {1, 3} {2, 3} {3, 3}

Let us define the events:
A = each made the same number of sales
B = Adams made exactly one sale
1. List the sample space for Event A and event B.
2. Find the total number of the sample space. S(n) =
3. Find the following probabilities:
(1) P(A) =
(2) P(B) =
(3) P(A∩B) =
(4) P(A∪B) =
(5) P(A|B) =

3.The statistician for a chain of 24 hour grocery stores in New York estimates that the probability that a customer who enters one of the stores between midnight and six a.m. will buy beer is 0.25. The probability that a customer entering the store during this time period will buy potato chips is 0.40. The probability that a customer entering the store during the this time period will buy both beer and potato chips is 0.10. What is the probability that a customer entering the store during this period will buy either beer or chips or both?

Answer 1