Unit 6 Probability & Simulation: the Study of randomness Simulation Probability Models General Probability Rules

Conditional Probabilities The conditional probabilty P(A|B) means the probability of A given that B has occurred. Slim is dealt a hand of four cards. Find the probability that he gets an ace. P(ace) = Find the conditional probability that slim gets another ace given he has an ace already in his hand. P(ace | 1 ace in 4 visible cards)

Given A=the grade comes from an EPS course B= the grade is below a B Find: P(B) P(B | A)P( A)P(A and B) Notice the following…

Downloading Music 20% of Internet users download music files, and 67% of downloaders say they don’t care if the music copyrighted. So the percent of users who download music and don't care about copyright is…

Slim wants diamonds Slim wants two diamonds in a row. Of the eleven cards he sees out on the table, four are diamonds. What is the probability he will get two diamonds in a row?

We can rearrange the general multiplication rule to get a formula for conditional probability.

What is the conditional probability that a grade at the University of New Harmony is a A, given that it comes from a liberal arts course? Use the formula to find the following… (and review it without the formula)

P(A and B and C) =

The future of high school athletes Only 5% of male high school basketball, baseball, and football players go on to play at the college level. Of these, only 1.7% enter major league professional sports. About 40% of the athletes who compete in college and then reach the pros have a career of more than 3 years. What is the probability that a high school athlete competes in college and then goes on to have a pro career of more than 3 years?

Online chat rooms are dominated by the young. If we look at adult Internet users only, 47% of the 18 to 29 age group chat, as do 21% of those aged 30 to 49 and just 7% of those 50 and over. Total 29% of adult Internet users are aged 18 to 29, another 47% are 30 to 49, and the remaining 24% are 50 or over. What is the probability that a randomly chosen user of the Internet participates in chat rooms?

The Multiplication Rule & tree diagrams The probability of reaching the end of any complete branch is the product of the probabilities written on its segments.

What percent of adult chat room participants are aged 18 to 29?