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) = .2 + .75 - .11 = .84

200

P(A) = .33, P(B) = .4, 

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

.33 + .4 = .73

300

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

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

.5*.75 = .375

400

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

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

.20 + .39 - (.20*.39) = .512

500

If two events, A and B, are mutually exclusive, what can we say about their independence?

A) They are independent

B) They are not independent

C) One cannot determine whether or not they are independent

B) They ARE NOT independent. If A and B are mutually exclusive, knowing that A has happened then makes it impossible for B to happen. Thus, A occurring influences the likelihood of B occuring.

Conditional

100

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

P(A)

200

60% of elm trees in Fargo get Dutch Elm Disease. If an elm tree gets Dutch Elm Disease, it has to be chopped down 80% of the time. Among elm trees without Dutch Elm Disease, just 5% have to be chopped down.

What is the overall probability that an elm tree in Fargo needs to be chopped down?

Tree Diagram!

0.6*0.8 + 0.4*0.05 = 0.5 or 50%

300

In probability notation, write out the following: the probability that a randomly selected student in the room is wearing a sweatshirt, given that student is boy.

P(sweatshirt|boy) = P(sweatshirt and boy) / P(boy)

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

In a bag of 20 flower seeds, 15 will produce a flower, and 5 are duds. Find the probability that the first seed that is a dud is the fourth one you pick without replacement. 

(15/20)*(14/19)*(13/18)*(5/17)

= 0.117

Random Variables

100

Discrete or Continuous?

X = time that 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.  Create a probability model for X.

X     |    0    |    1    |    2    |

P(X) |  .25   |   .5    |   .25  |

300

Find the expected value for the game:

Roll a six-sided die,

If you roll a 1, win $10

If you roll a 2, 3, or 4, lose $15

If you roll a 5, win $20

If you roll a 6, win $50

10*(1/6) + -15*(3/6) + 20*(1/6) + 50*(1/6)

= $5.83

400

Let X = height of students  at FNH, in inches, 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 AND standard deviation for the random variable X = years taken to graduate at NDSU.

X     |   3  |   4  |   5  |   6  |   7 |

P(X) | 0.1 | 0.5 | 0.1 | 0.2 | 0.1 |

Expected value: 4.7 years

Standard deviation: 1.1874

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 = $1.80

sd_x = $0.70

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

$2.80, $0.70

300

Let A and B be random variables

mean_A = 6.4

mean_B = 8.9

Find mean_{A and 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

Geometric is always concerned with the first occurrence of an event happening, while binomial is concerned with a number of successes within a set number of trials

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)

30 C 5 * (0.25)^5 * (0.75)^15

.1047

400

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

0.4 + 0.6*0.4 + 0.6*0.6*0.4 

= 0.784

500

You are able to talk Mr. Lehman into extending a homework assignment 95% of the time. Out of 10 homework assignments, what is the probability that you can talk him out of at least 9 of them?

0.913

(I'm not even going to attempt to type in the work)