Finite Math Midterm

Directions:
This is a 25 question test covering material from chapters 1-4. Each question is worth 4 points. You should be able to complete the test within 90 minutes. You may continue taking the test after the timer has reached 0, but take note that on the real midterm you would have to turn the test in as is. Once you submit the test it will automatically be graded for you and links will be provided to an instructional video explaining how each problem is done in detail. Hit the start button when you are ready. Good luck.

Date: March 26, 2017
90:00
Start Test
1.

A box contains 3 nickels and 4 quarters. Two coins are selected simultaneously and at random, and a random variable X is defined as the total value (in cents) of the two coins selected. Find the probability Pr[X=50].

A) 2/7

B) 1/7

C) 3/7

D) 1/2

E) none of the others

2.

An unfair die has the property that when rolled, each of the odd numbers is equally likely to land uppermost, each of the even numbers is equally likely to land uppermost, and each odd number is three times as likely to land up as even number. The die is rolled and the result is noted. Find the probability that the result is in the event {1, 3, 6}.

A) 1/12

B) 3/12

C) 5/12

D) 7/12

E) none of the others

3.

There are 10 CDs in a rack; 6 are jazz and 4 are classic rock. Two CDs are selected at random, one after the other without replacement, and the type of each is noted. Find the probability that the first is jazz given that at least one is jazz.

A) 1/10

B) 4/10

C) 5/26

D) 9/13

E) none of the others

4.

An unfair coin with Pr(H) = .7 is flipped 4 times and the result of each toss is noted. What is the probability that there are at least three heads? (choices in formulas).

A) C(4,3)(.7)^3(.3)

B) C(4,3)(.7)^3(.3) + C(4,4)(.7)^4

C) C(4,3)(.7)(.3)^3 + C(4,4)(.3)^4

D) C(4,3)(.7)(.3) + C(4,4)(.7)

E) none of the others

5.

Let A and B be subsets of a universal set U: n(U) = 50, n(B) = 20, and n(A U B') = 40. Find n(A ∩ B).

A) 2

B) 5

C) 10

D) 20

E) none of the others

6.

A box contains 3 red balls and 4 blue balls. Two balls are selected at random, one after another without replacement, and the color of each is noted. Find the probability that the first was red given that the second was blue.

A) 1/2

B) 1/7

C) 2/7

D) 4/7

E) none of the others

7.

Suppose the free throws of a basketball player can be viewed as Bernoulli trials all with success probability p=.3. If he takes five shots in a game, and if each successful shot is worth 2 points, find the expected number of points scored.

A) 1

B) 2

C) 3

D) 4

E) none of the others

8.

A fair coin is flipped until a tail follows a head or a total of four flips, and the result of each flip is noted. The event E consists of those outcomes with exactly 2 heads. Find Pr(E).

A) 1/10

B) 1/5

C) 1/2

D) 1/4

E) none of the others

9.

Amy, Bob, Carlos, Debra, and Erin have tickets for five adjacent seats at a concert. In how many ways can they be seated if Amy is in the middle and Bob is sitting next to her?

A) 14

B) 2

C) 11

D) 12

E) none of the others

10.

A product code is to be formed with three distinct letters from the set {T, C, H, B, I}. How many different product codes are there? Note: BIT is a different product code than TIB.

A) 10

B) 30

C) 60

D) 120

E) none of the others

11.

Suppose that for Joe the events "late for class" and "prepared for class" are independent events with Pr(late for class) = .3 and Pr(prepared for class) = .7. What is the probability that he is late but prepared?

A) .21

B) .3

C) .42

D) .5

E) none of the others

12.

A sample space has 4 outcomes with weights w1, w2, w3, w4. If w1 = 2w2, w2 = 2w3, w3 = w4, find w4.

A) 1/14

B) 1/8

C) 1/4

D) 2/7

E) none of the others

13.

Three students are selected simultaneously and at random from a group consisting of 3 freshmen, 2 sophomore, and 2 juniors. Find the probability that the 3 students are from 3 different classes.

A) 1/35

B) 3/35

C) 8/35

D) 12/35

E) none of the others

14.

70 students were asked about their plans for the weekend. 30 plan to go to a football game, 40 plan to attend a concert, and 20 plan to do both. How many plan to do neither?

A) 10

B) 15

C) 20

D) 30

E) none of the others

15.

Let U = {I, T, S, H, C, K, F, U}, E = {S, H, C, K}, F = {C, K, F, U}, and G = {T, S, H, K}. Find (E U F) ∩ G'.

A) {C, F, U}

B) {C, F}

C) {F, U, K}

D) {T, F, K}

E) none of the others

16.

There are two coins, coin 1 has Pr(H) = .4 and coin 2 has Pr(H) = .7. A coin is selected at random and flipped. If the result is H, what is the probability coin 1 was selected?

A) 1/11

B) 4/11

C) 6/11

D) 1/2

E) none of the others

17.

Let E and F be events in a sample space with Pr(E) = .7, Pr(E ∩ F) = .3, and Pr(F) = .5. Find Pr(E|F).

A) 1/5

B) 2/5

C) 1/2

D) 3/5

E) none of the others

18.

A random variable X has the probability density function shown below. Find the expected value of X.

density function

A) .1

B) .2

C) .5

D) 1

E) none of the others

19.

There are 2 male roles in a play and there are 4 males auditioning for these roles, including Alex. Also there are 2 female roles in the same play and there are 5 females auditioning, including Zelda. If each person is equally likely to be assigned a role, find the probability that exactly one of Alex or Zelda is assigned a role in the play.

A) 1/7

B) 1/2

C) 2/7

D) 4/7

E) none of the others

20.

A box contains 7 balls with numbers 1 through 7. Two balls are drawn simultaneously and at random and the numbers on the balls are noted. Find the probability that the sum of the numbers is at least 4.

A) 20/21

B) 1/7

C) 1/2

D) 1/21

E) none of the others

21.

A menu in an Italian restaurant has 4 kinds of salads and 7 toppings for pizza. A student plans to order a meal consisting of a salad and a pizza with 2 different toppings. Find the number of different meals available.

A) 48

B) 56

C) 72

D) 168

E) none of the others

22.

A group of 7 students consists of 4 freshman and 3 sophomores. Two students are selected at random. Find the probability that both are freshmen given that at least 1 is a freshman.

A) 1/7

B) 1/3

C) 1/2

D) 5/7

E) none of the others

23.

Suppose A is the set of Purdue students who are ugly and B is the set of students who are stupid. Which set describes those Purdue students who are ugly but not stupid?

A) (AUB)’

B) A∩B’

C) A∩B

D) A’∩B

E) none of the others

24.

Box A contains 3 red balls and 1 green ball and box B contains 3 red balls and 3 green balls. A box is selected at random, then a ball is drawn at random from that box and its color is noted. Find the probability that the ball is red.

A) 5/8

B) 1/2

C) 3/8

D) 7/8

E) none of the others

25.

A guy has gotten six phone numbers last night, and he plans to call 3 of them today and 3 tomorrow. In how many ways can he choose the 3 girls to call today?

A) 3

B) 10

C) 20

D) 120

E) none of the others