Conditional Probability
What is the equation for conditional probability?
P(B|A) = P(A and B)/P(A)
When two events are independent, P(A|B) is equal to _____
P(A)
Determine whether or not the events are disjoint:
A card is randomly selected from a standard deck of 52 playing cards. What is the probability that it is a 4 card or a diamond?
Not disjoint - Overlapping
Permutations and combinations are similar, but in which one does order matter?
Permutations
Francisco asks the students in his school what pets they have. He studies the events shown.
Event S: the student has a cat
Event T: the student has a dog
Francisco finds that the two events are independent.
Select all the equations that must be true.
1,4,6
P(A) = 0.40 and P(B)= 0.30
Find P(A|B) given that A and B are independent events
P(A|B) = 0.40
Determine whether or not the events are independent:
Ben is taking a practice OST and randomly guesses the answer to four true-false questions. Determine whether guessing the correct answer to Question 1 and guessing the correct answer to Question 2 are independent events.
The events are independent
Determine whether or not the events are disjoint:
A card is randomly selected from a standard deck of 52 playing cards. What is the probability that it is an 8 or a face card?
Disjoint
In how many different ways can you arrange the letters in the word “JULY”?
4! = 24
The probability of flipping a fair coin and heads landing face up is 0.5. The probability of rolling a fair number cube, with sides numbered 1 through 6, and an odd number landing face up is 0.5.
What is the probability of flipping heads or rolling an odd number?
3/4 = 0.75 = 75%
A school lunch offers three different fruits and two different vegetables as side dishes. You are served two different side dishes at random. Find the probability that you are served a vegetable second given that you are served a fruit first.
50%
Determine whether or not the events are independent:
Jaydah is eating Skittles Littles. She does not like 3/6 of the flavors. There is one of each flavor in a bag. Determine whether pulling a good flavor first and a bad flavor second are independent events.
Dependent Events
P(A) = 0.81 and P(B) = 0.12. A and B are disjoint events. When is P(A or B)?
P(A or B) = 0.93
5c1 =
5
Two events, A and B are independent.
P(A) = 0.3
P(A and B) = 0.24
What is P(B)?
0.8
At Toledo Early College, 60% of students buy school lunch, 18% of students buy a dessert, and 10% of students buy a lunch and a dessert.
What is the probability that a student buys dessert given that they buy lunch?
1/6 = 0.167 = 16.7%
Are events A and B independent or dependent?
P(A) = ½ ; P(B) = ⅓ ; P(A and B) = ⅙
Independent
P(A) = 0.43 and P(B) = 0.52. A and B are overlapping and independent events. What is P(A or B)?
P(A or B) = 0.7264
6p5 =
720
The probability of event A is 0.6. The probability of event B is 0.7. A and B are independent events. What is the probability of A and B?
0.42
At Toledo Early College, 60% of students buy school lunch, 18% of students buy a dessert, and 10% of students buy a lunch and a dessert.
What is the probability that a student buys lunch given that they buy dessert?
5/9 = 0.556 = 55.6%
Are events A and B independent or dependent?
P(A) = 1/4 ; P(B) = 1/5 ; P(A|B) = 1/5
Dependent
An archeology lab receives 150 artifacts for processing. Of those, 108 are either made of clay or have coloring. There are 81 artifacts made of clay and 34 artifacts that have coloring. What is the probability that a randomly selected artifact is made of clay AND has coloring.
P(A and B) = 0.047
How many different ways can you arrange 2 of the letters in the word "FLOWER" ?
30
221, 119, 171, 189, 360, 392, 308