probability

Question 1

What does “not” mean

Answer 1

subtract from 1. i.e.: if p(blue eyes) = 70%, then P(not blue eyes) = 1 - .7 = 30%

Question 2

what is the law of large numbers?

Answer 2

Theorem that tells us that as the number of independent trials increase, that the results will become closer and closer to the theoretical probability

Question 3

law of averages

Answer 3

misunderstanding of the law of large numbers: thinking that if a good hitter has struck out 3 times that he is “due” for a hit. The law of large numbers works only in the long run, not in the short term.

Question 4

empirical probability

Answer 4

P(A) = (# times A occurs)/(total # trials) in the long run

Question 5

first three rules for working with probability

Answer 5

1, make a picture

2. make a picture
3. make a picture

Question 6

If S = your sample space, then

P(S) =

Answer 6

ONE!!!

Question 7

disjoint events

Answer 7

events that have no outcomes in common. for example, choosing a freshman, and choosing a sophomre from a mixed group of students would be disjoint events.

Question 8

Addition Rule (disjoint events)

Answer 8

for two disjoint events, A and B, the probability that one OR the other occurs is the sum of the probabilities of the two events.
P(A U B) = P(A) + P(B), A and B disjoiont

Question 9

Multiplication Rule (independent events)

Answer 9

If two events A and B are independent, that the probability of both A AND B occurring is the product of the two probabilities
P(A and B) = P(A) times P(B), A and B independent

Question 10

General Addition Rule:

P(A or B), events not disjoint

Answer 10

P(A) + P(B) - P(A and B)

Question 11

Are the events “heart” and “black jack” disjoint? independent?

Answer 11

“heart” and “black jack” have no common outcomes (there are no black jack of hearts!) so they are disjoint. However, they are not independent. P(black jack) = 2/52, but the P(black jack/lheart) = 0!

Question 12

What is expected value?

Answer 12

The mean. What you would average if you played the game A LOT!

Question 13

What is the mean of a random variable?

Answer 13

The expected value. The sum of the probabilities times the values.

Question 14

Can disjoint events be independent?

Answer 14

NO! IF the are disjoint, then knowing one tells you that the other could not happen. Therefore they are NOT INDEPENDENT

Question 15

You own a tire shop, and order tires from two companies, A and B. 80% from A and 20% from B. 1% of tires from A are defective, and 4% from B are defective. What strategy would you use to determine the probability that a defective tire comes from A?

Answer 15

Make a tree diagram!

Question 16

What is the probability that your first success occurs on the 7th try?

Answer 16

(q^6)(p)

Question 17

What is a probability model?

Answer 17

All possible values of the random variables with their respective probabilities.

Question 18

When combining probability models, do you add or subtract standard deviation?

Answer 18

Neither! Square the standard deviations, add them, then take the square root.

Question 19

What is the probability of at least one?

Answer 19

1 - (probability of none)

Question 20

What does the geometric model tell us?

Answer 20

About the first success. Example: what is the likelihood the first success is on the fifth trial?