# probability Flashcards

1
Q

What does “not” mean

A

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

2
Q

what is the law of large numbers?

A

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

3
Q

law of averages

A

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.

4
Q

empirical probability

A

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

5
Q

first three rules for working with probability

A

1, make a picture

1. make a picture
2. make a picture
6
Q

If S = your sample space, then

P(S) =

A

ONE!!!

7
Q

disjoint events

A

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.

8
Q

A

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

9
Q

Multiplication Rule (independent events)

A

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

10
Q

P(A or B), events not disjoint

A

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

11
Q

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

A

“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!

12
Q

What is expected value?

A

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

13
Q

What is the mean of a random variable?

A

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

14
Q

Can disjoint events be independent?

A

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

15
Q

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?

A

Make a tree diagram!

16
Q

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

A

(q^6)(p)

17
Q

What is a probability model?

A

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

18
Q

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

A

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

19
Q

What is the probability of at least one?

A

1 - (probability of none)

20
Q

What does the geometric model tell us?

A

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