A jar contains seven black balls, numbered 1 to 7 , and six white balls, numbered 1 to 6. A ball is chosen at random from the jar. Find the probability that:

a. the ball is white.

b. the ball is odd-numbered.

c. the ball is white or odd-numbered.

d. the ball is white, given that it is odd-numbered.

e. What if balls are chosen at random from the jar, without replacement? 2

Find the probability that both balls are black.

4. Skyline high school students were surveyed about what types of club events they attended last year. 50% attended robotics competitions, 56% attended math competitions, 61% attended science competitions, 18% attended both robotics and math competitions, 37% attended both math and science competitions, 19% attended both robotics and science competitions , and 7% attended all three types of competitions.

a. [3 pts] Draw A Venn diagram representing the survey results.

b. Find the probability that a person attended: none of the events

c. Find the probability that a person attended:only robotics and science competitions.

5. [5pt] Given the word TAYLOR:

a. How many permutations are there? a. _______________

b. What is the probability that a random permutation will have L and R next to each other?

c. What is the probability that a random permutation will start with T and end with R?

6. [4pt] Meg has a bag with 6 pink marbles and 2 green marbles. She is going to roll a four-sided die that has A on one face and B on the other three faces. If she rolls an A, she will add 2 green marbles to the bag. If she rolls a B, she will add 1 pink marbles to the bag. After adding the marbles, Meg will then draw one marble from the bag.

a) [2] Draw the tree diagram representing the scenario.

b) [2] What is the probability Meg rolled A given that she draw a green marble.

7. There are 8 trumpet players and 5 flute players in the school band. A group of three trumpet plays and three flute players will be selected to represent the band at a festival.

a. In how many different ways can group be selected? [ 2 pts ] a. _______________

b. Susan is the bet trumpet player and John is the best flute player. In how many different ways can the group be selected if it must include both of them? [2 pts] b. _______________

c. What is the probability that the group includes both Susan and John?