Office: 231 Ketter Hall Phone: (716) 643-4365 Email: qw6@buffalo.edu shraf Fathi

Question

Office: 231 Ketter Hall Phone: (716) 643-4365 Email: qw6@buffalo.edu shraf Fathi Ali Solimap): T 1:00PM-3:00PM.(Amrl Homework # 3: Counting Methods and Probabilities of Random Variables Office hours: Instructor (Oian Wang): M.T W THE: 11.:00-11:50AM, Ketter 231 TAs (an Rahimi, and Amr A Dae date: Before the class starts on September 17 (Mon), 2018 Six problems in total related to Chapter 2 of the textbook: 1 Powerball lottery is played by picking five numbers (called white balls) from 1 to 69 and one Powerball number (called red ball) from 1 to 26. Assuming balls are drawn randomly and independently of each other and we do not consider the Power Play option, answer the following questions a) In how many ways the six numbers (five white balls + one red ball) can be drawn? b) What is the probability to win the Jackpot by matching all the six numbers, given that you only purchase one set of numbers? What is the probability to win SI million by matching the five white ball numbers, given that you only purchase one set of numbers? c) What is the probability to win $50,000 by matching four white ball numbers and the red ball number, given that you only purchase one set of numbers? d) 2. Exercise 6 for Section 2.2 in the textbook (pp. 68) 3. Exercise 10 for Section 2.2 in the textbook (pp. 69) 4. Let X represent the number of tires with low air pressure on a randomly chosen car. Three probability distribution (or mass) functions are built as shown in the following table. Answer the following questions: pifx) 0.2 0.2 0.3 0.3 0.2

Explanation / Answer

Power ball lottery with 5 white balls (1 to 69 ) and 1 power ball number ( 1 to 26)

   First number in 69 ways

Second number in 68 ways

Third number in 67 ways

Fourth number in 66 ways

Fifth number in 65 ways

Sixth number in 26 ways

Total =69*68*67*66*65*26 ways =35064160560

2.Probability to win = 1/69*68*67*66*65*26

                           =1/35064160560

3. no. of ways to match 5 white balls and not matching red ball is 25

Probability to win= 25/35064160560

4. No. of ways to match 4 white balls and one red ball is 64

Probability to win =64/35064160560

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