Name:Algebra 2

Date:

Homework: Counting and Probability

1.A state runs a lottery called “Pick 6.” A player buys a lottery ticket showing 6 of the numbers from 1 through 40. For example, a ticket could look like this:

4 - 11 - 17 - 25 - 26 - 38

At the end of the day, 6 of the numbers from 1 through 40 are picked as winners, and anyone whose ticket shows those numbers wins a big prize. (The order of the numbers on the ticket does not matter, the winner just has to have the right set of numbers.)

What is the probability of winning the “Pick 6” lottery? Express your answer first as a fraction, then as a decimal.

2.A school jazz band has 5 juniors and 7 seniors. Free tickets to a jazz concert are distributed to 3members chosen at random.

a.What is the probability that all 3 tickets are received by seniors? [Hints: How many total ways can the tickets be distributed? How many ways can the tickets be distributed with only seniors getting them?]

b.What is the probability that all 3 tickets are received by juniors?

c.Suppose that Sungyoon is one of the seniors in the band. What is the probability that Sungyoon will get one of the tickets?

d.Suppose that Jane, John, and June are three of the juniors, and they are hoping to go to the concert together. What is the probability that all 3 of the tickets will go to these 3 students?

3.There are 100 tickets for a raffle drawing. John, Ron, and Levon each hold one of the tickets. A 1st prize, a 2ndprize, and a 3rd prize will be given to the holders of 3 different tickets.

a.What is the probability that the raffle outcome will be: Jon wins 1st prize, Ron wins 2ndprize, and Levon wins 3rd prize?

b.What is the probability that the three prize winners will be Jon, Ron, and Levon?

4.Suppose you have a set of 10 cards numbered 1-through-10, and you randomly pick 3 of the cards. Find the probability…

a.that the three cards chosen are the “4”, the “7”, and the “10”

b.that the cards chosen are the “4”, the “7”, and any other card

c.that all three cards chosen have even numbers

d.that none of the three cards have a prime number (2, 3, 5, 7)