Vocab 1
Vocab 2
Probability Problems
Practice Problems
Conditional Probability
100
Define Union("or")/P(A ∪ B)
The event that at least one event occurs
Ex: Suppose set A = {1, 2, 3} and set B = {1, 3, 5}. Then, the union of sets A and B would be {1, 2, 3, 5}.
100
Define independence in terms of two events
Two events A and B are independent if the occurrence of one event has no effect on the chance that the other event will happen. In other words, events A and B are independent if
P(A | B) = P(A) and P(B | A) = P(B).
100
If you randomly roll a six-sided dice, what is the probability you land on an even number?
3/6 or 1/2
100
Probability of flipping two heads in a row:
.5x.5=.25
100
The table below shows the data of 3 pointers made and missed in last weeks boys/girls basketball game.
Made Missed Total
Girl 3 8 11
Boy 6 13 19
Total 9 21 30
Determine the probability of only a girl making a 3 pointer.
3/11
200
Intersection("and")/P(A ∩ B)
The event that all the events occurs.
Ex: set A = {1, 2, 3} and set B = {1, 3, 5}. Then, the intersection of sets A and B would be {1, 3}.
200
Define conditional probability
Conditional probability is the probability of an event, given some other event has already occurred.
200
You are taking a multiple choice test, all with 4 possible answers. If you had no idea what the answer was, what is the probability of you guessing the correct answer?
1/4
200
Age: 10 20 30 40
Probability: 0.57. 0.17 0.14 0.12
Show that this is a legitimate probability model.
0.57 + 0.17 + 0.14 + 0.12 = 1
200
The table below shows the data of 3 pointers made and missed in last weeks boys/girls basketball games.
Made Missed Total
Girl 3 8 11
Boy 6 13 19
Total 9 21 30
Determine the probability of made threes in last weeks game.
3/10
300
The probability of any outcome is between these two numbers
0 and 1
ALSO: All possible outcomes together must have probabilities whose sum is 1.
300
What's the difference between sampling with replacement rather than sampling without?
When we sample with replacement, the two sample values are independent.
In sampling without replacement, the two sample values aren't independent.
300
If every letter in the alphabet is placed into a bag, that are the odds that you will select a letter found in the word "Foggy"?
4/26 or 2/13
300
Age: 10 20 30 40
Probability: 0.57. 0.17 0.14 0.12
Find the probability of students that aren't 10 years old.
1-.57=.43
300
The table below shows the data of 3 pointers made and missed in last weeks boys/girls basketball game.
Made Missed Total
Girl 3 8 11
Boy 6 13 19
Total 9 21 30
Determine the probability of the player hitting a three pointer and being a boy.
P(A and B)= 2/10
400
Define Event
An Event is one or more outcomes of an experiment
Ex: When a number cube is rolled, 1, 2, 3, 4, 5, or 6 is a possible event.
When you roll a number cube and toss a coin at the same time, a possible event is a 3 and a tail respectively.
400
Define the complement of an event
The probability that the event does NOT occur
NOTE: Compliment rule is 1-P(A)
400
A cooler has 8 cans of soda; 3 cokes, 3 sprites, and 2 root beers. If you reach into the cooler, what are the odds that you will pick a diet soda?
0/8
400
P(online)=
.93
400
The table below shows the data of 3 pointers made and missed in last weeks boys/girls basketball game.
Made Missed Total
Girl 3 8 11
Boy 6 13 19
Total 9 21 30
Determine the probability of the person shooting a three pointer is a girl.
11/30
500
Define disjoint or an event that is mutually exclusive
Events that are disjoint have no outcomes in common. They cannot occur at the same time.
Ex: During a coin toss, getting a head and tail are two disjoint events.
500
Define the law of large numbers
If we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single value.
500
If every letter in the alphabet is placed into a bag, that are the odds that you will select a vowel? (not Y)
5/26
500
P(online|profile)=
.55
500
The table below shows the data of 3 pointers made and missed in last weeks boys/girls basketball game.
Made Missed Total
Girl 3 8 11
Boy 6 13 19
Total 9 21 30
Determine the probability of the person shooting a three pointer is a boy.
19/30