AP Statistics Probability

Basic

100

P(A) = .2, P(B) = .75, P(A and B) = .11

Find P(A U B)

P(A U B) = .84

200

P(A) = .33, P(B) = .4, 

Find P(A or B) if events A and B are mutually exclusive

.73

300

P(A) = .5, P(B) = .75

Find P(A and B) if the events are independent.

.375

400

P(A) = .20, P(B) = .39

Find P(A or B) if events A and B are independent

.512

500

If two events are mutually exclusive, what else can you determine? (Needs a justification)

A) They are independent

B) They are not independent

C) One cannot determine whether or not they are independent

B. 

If one event happens, the other one is determined - it cannot happen.

Conditional

100

P(A given B) = 

P(A and B) / P(B)

200

If events A and B are independent, P(A given B) = 

P(A)

300

Find the probability that a randomly selected student in the room is wearing a sweatshirt, given that student is wearing blue.

P (sweatshirt given blue) = P (sweatshirt and bluee) / P(blue)

400

Find the probability that a card randomly selected from a standard deck is a queen, given the card is black.

2/26

= .077

500

Find the probability that the sum of two dice is greater than 8, given the sum is even.

4/18

= .222

Random Variables

100

Discrete or Continuous?

# of hours students spend on AP Statistics homework

Continuous

200

Let X be a random variable where X = the number of heads flipped in 2 coin flips.  Find P(X = 2)

1/4

300

Find the expected value for the game:

Roll a six-sided die,

If < 2, win $10

If > 5, win $20

10(1/6) + 20(1/6)

10/6 + 20/6 = 30/6 = 5

400

Let X = height of students, in inches,at FHS, and the distribution is approximately normal.  If the mean and standard deviation are 52 and 4.7, respectively, find the probability that a randomly selected student would be taller than 60 inches.

.0444

500

Find the expected value of the game:

Roll 2 dice,

Sum < 5, win $40

Roll a double, win $85

18.611

Transforming/Combining Random Variables

100

X = Random Variable

mean_x = .12

sd_x = .38

Multiply each X value by 10, find the new mean and sd

1.2, 3.8

200

X = $ amount of each size soda (random variable)

mean_x = 1.8

sd_x = .7

Find the new mean and sd if the store increases their prices of soda by $1 each

2.8, .7

300

Let A and B be random variables

mean_A = 6.4

mean_B = 8.9

Find mean_{A + B}

15.3

400

X and Y are Random Variables

sd_x = 8

sd_y = 7

Find sd_x-y

sqrt(113) = 10.63

500

Let U and V be random variables that are approximately normally distributed.  

mean_u = 500, sd_u = 15

mean_v = 200, sd_v = 8

Let T = U + V, find P(T > 717)

.16

Binomial and Geometric

100

The difference between binomial and geometric settings

Binomial require a fixed number of trials. Geometric stops when the first success happens.

200

Tim makes 80% of his free throws.  In a game, he takes 14 free throw attempts.  Find the mean and standard deviation of the distribution

mean = (.8)(14)

SD = sqrt(14x.8x.2)

300

You take a 30 question multiple choice test (choices A-D for each question), and unfortunately know nothing on it.  If you were to guess on every question, what is the probability that you get 5 questions correct?

binomialpdf(30,.25,5)

.1047

400

A wide receiver has a catch rate of 40%.  What is the probability that his first catch will be before his 3rd target?

geometriccdf(.4,2)

500

The AP Stats Midterm Exam has 100 multiple choice questions (A-E choices).  Wanda hasn't payed attention all year and guesses on every single one of them.  If X is the # of questions correct, find P(X>22).

Use binomial/geometric or normal depending

.3085