Empirical Probability

The accuracy of empirical probability depends on the number of trials. The Law of Large Numbers says that the more times an experiment is performed, the more accurately the probability can be used as a predictor.

2004 9th Grade32) A spinner was spun 20 times. The results are shown in the table below.Which color on the spinner has the same experimental probability as theoretical probability?A RedB WhiteC BlueD Yellow

The answer is B

Circular ModelFind the empirical probability of hitting the

shaded area of the circle.

Circular Model, cont.Use the given measurements on the circle to

mathematically calculate the area of the whole circle.

…the area of the shaded sector of the circle.

Find the ratio of the area of the shaded sector of the circle to the area of the whole circle.

Which type of probability does this represent, empirical or theoretical?

2006 Summer Exit16) A total of 550 students from the Fairfield High School junior class voted on their choice for their seniorclass gift to the school. The table below shows the results of the vote.Which graph best represents the results of the survey?

Answer is F

2004 Summer Exit28) Marcos has a spinner with 12 equal sections colored either blue or red. If the spinner lands on blue on 33 out of 50 spins, which is most likely the number of blue sections on the spinner?A 4B 6C 8D 10

The answer is C

MedcoMeds tested a new cholesterol medicine that was meant to lower levels of bad cholesterol. The medication was given to 500 individuals with the following results:

Cholesterol lowered ----------------------- 260Cholesterol increased -------------------- 82Cholesterol stayed the same ----------- 158

a. Why is this considered empirical probability?b. Find P (lowered cholesterol levels).c. Find P (increased cholesterol levels).d. Find P (cholesterol levels stayed the same).e. How could the approximation of the probability be improved?

Why would this be important in this situation?

Mind map

JAW BREAKERS VENN DIAGRAMThe following represents a bin that contains 75 jaw breakers in the colors red, blue, and green. Consider one jaw breaker selected from the bin.

Mutually exclusive events.

SOMETHING SMELLS A LITTLE FISHY VENN DIAGRAMCertain species of fish in the coastal areas can be found only in salt water, others only in fresh water, and others in both or brackish water. A total of 100 fish was taken as a sample representation for a coastal area. Fish were taken from the Nueces River (fresh water), Nueces Bay (brackish water), and Corpus Christi Bay (salt water). Consider one random fish from a coastal area.

Not mutually exclusive

Mutually Exclusive for Events

Addition RuleP(A or B) = P(A) + P(B)

For Events That Are Not Mutually Exclusive

Addition RuleP(A or B) = P(A) + P(B) – P(A and B)

Example:

Multiplication Rule

P(A and B) = P(A) ● P(B)

P(5 on the die and heads on a coin)

Conditional Probability

P(A|B)Probability that A will occur given that B has

already occurred

P(of drawing a two then a three from the deck of cards)

Study a deck of 52 playing cards. Find the probability of drawing a card that is a queen given each of the following conditions. Cards will not be replaced after the first draw.

a. P(Queen)

b. P(Queen |the card is a face card)

c. P(Queen |Queen was not drawn on first draw)

d. P(Queen |Queen was drawn on first draw)