The probability of an event given another event has occurred. Typically this will change the sample space as seen below.
Adapted from https://resources.corwin.com/sites/default/files/lesson_7.1_worksheet_1.pdf
1. What do you know about drug testing?
2. Theoretical situation: Assume that a certain drug test is 98 percent accurate. This means 98 percent of the people who used the drug will test positive and 98 percent of the people who did not use the drug will test negative. Also assume that only 5 percent of people on the job (1 in 20) engage in drug use.
Liquid Gold: Pain Doctors Soak Up Profits By Screening Urine For Drugs (Schulte & Lucas, 2017)
Racism, Again: Why Drug Tests Are Helping Black Americans Get Jobs Rosen, 2014)
A rare disease infects 1 out of every 1000 people. A lab test is 99.8% accurate to indicate if a person has the disease or not.
You just received a positive test. What is the probability that you have the disease? [source]
P(has disease | positive test) ~= 33.3%
(Hints: Assume 1,000,000 people. Complete the two-way frequency table below.)
|Has disease||No disease||Totals|
P(vaccinated | infected) vs. P(infected | vaccinated)
What is the probability of rolling a sum of 2 on two six-sided dice? P(2) = 1/36
What is the probability of rolling a sum less than or equal to 5? P(sum ≤ 5) = 10/36
What is the probability of rolling a sum of two, given the roll was less than or equal to 5? P(2 | sum ≤ 5) = 1/10
Mr. Jones has two children, at least one of which is a boy. What is the probability the other child is a boy? (1/3)
Mr. Smith has two children and the eldest is a boy. What is the probability that both children are boys? (1/2)
Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors? switching gives 2/3 probability, not switching gives 1/3; see 21 (2008 film)
See Cut-the-knot for more information