Formulas
P(A and B) = P(A|B)P(B)
What is the Product Rule?
A bag contains 8 red marbles and 4 blue marbles. You randomly pull a marble without replacement and then a second marble. The first is red and the second is blue.
What are dependent events?
Let A denote the event for which the two faces sums to 10, and B the event for which the first throw equals 5.
Then the sample space for A is {(5,5),(4,6),(6,4)}.
The sample space for B is {(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}.
This is P(B|A).
What is 1/3?
You've decided you want a plant for your room. At the gardening store, there are 4 different kinds of plants (tulip, fern, cactus, and ficus) and 4 different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).
This is the probability of randomly choosing a tulip in a plastic pot.
What is 1/16?
Conditional Probability
What is P(A|B) = P(A and B)/P(B)?
You flip a coin and then roll a six-sided die. The coin lands heads-up and the die shows a one.
What are independent events?
Susan took two tests. The probability of her passing both tests is 0.6. The probability of her passing the first test is 0.8.
This is the probability of her passing the second test given that she has passed the first test.
What is 0.75?
There are 27 students available to represent the upperclassmen at a fair. 13 are Juniors and 14 are Seniors.
This is the probability that the first one chosen will be a Senior and the second one will be a Junior.
What is 7/27?
Independence in terms of conditional probability
What is P(A|B) = P(A) or P(B|A) = P(B)?
A cooler contains ten bottles of Gatorade - 4 lemon-lime, 3 orange, and 3 fruit punch. You pull a random bottle out the cooler, replace it and shuffle the bottles around. You repeat this process twice. The first time results in pulling lemon-lime. The second and third times result in pulling fruit punch.
What are independent events?
This is the probability that the total of two dice will be greater than 9, given that the first die is a 5.
What is 1/3?
There are 45 men on the roster of the football team. 3 are quarterbacks, 10 are offensive lineman, 6 are defensive lineman. 4 are running backs, 6 are linebackers, 8 are defensive backs, 1 is a kicker and the rest are receivers.
This is the probability that two players chosen at random would be a QB and a receiver.
What is 1/60?