Introduction to Probability
If there is a spinner with 12 equal sectors, what is the probability that the spinner will land on an even number?
1/2 or 50%
The set A is all interegers that are odd and less then 10. Write set A in roster form.
(1,3,5,7,9)
A= {2,3,4,7,8,9}
B= {1,2,4,5,6,8}
What is the Union of A or B?
A u B= {1,2,3,4,5,6,7,8,9}
Male Female Total
Going to College 12 18 30
Not Going 15 16 31
Total 27 34 61
If a person was picked at random, what is the probability that they're male?
n(M)/n(S)=
27/61=
.44 or 44%
Where did Ms. Brito go to high school?
Dominican Academy!!!!!
If a coin is flipped four times, what is the probability that the coin will land on heads all four times? (Hint: use a tree diagram)
1/16
Set A: {1,2,3,4,5,6,7,8,9}
If set B is all elements of A that are odd and set C is all elements of A that are multiples of 3, what would be the intersections?
3 and 9
A= {2,3,4,7,8,9}
B= {1,2,4,5,6,8}
What is the intersection of A and B?
A n B= {2,4,8}
Male Female Total
Going to College 12 18 30
Not Going 15 16 31
Total 27 34 61
If a person was picked at random, what is the probability that they're going to college?
n(C)/n(S)=
30/61=
.49 or 49%
Where did Ms. Brito go to college?
NYU
Fun Fact: She first attended St. John's and then transferred to NYU.
Soda Number who Preferred
A 15
B 23
C 13
Total 51
What is the empirical probability that a person selected at random from this group would prefer soda C?
13/51 or .25 or 25%
If we flip a coin and roll a six-sided die, write a set of ordered pairs that represents the outcomes of this experiment.
S= {(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
There are 12 outcomes.
A= {2,3,4,7,8,9}
B= {1,2,4,5,6,8}
Using sets A and B, verify the addition law for the union of two sets.
n(A or B)=n(A)+n(B)-n(A and B)
9=6+6-3
9=9
Male Female Total
Going to College 12 18 30
Not Going 15 16 31
Total 27 34 61
If a person is picked at random, what is the probability that a female in picked that does not go to college?
n(F and N)/n(S)=
16/61=
.26 or 26%
What is Ms. Brito's favorite color?
Blue
What is theoretical probability?
You do not have to run the experiment to determine the probability of an event.
If the probability that you will draw a green jellybean from a bag is 4/13 what is the probability that you will not draw a green jellybean from the bag? (Show your work)
P(G)+P(not G)= 1
4/13+P(not G)=1
13/13-4/13= 9/13
A survey at Dominican Academy showed that 76 students enjoyed going to the movie theater and 31 students liked staying home to watch movies. 16 students enjoyed doing both. How many students liked only going to the movie theater? How many students only liked staying home to watch movies?
50 liked only going to the movie theater.
15 only liked staying home to watch movies.
Kaylyne played two soccer games. The probability of her winning both games is 0.86. The probability of her winning game A is 0.88. What is the probability of her winning game B given that she won game A?
P(game B, game A) = P(A and B)/P(A)
.86/.88= .98 or 98%
In which borough did Ms. Brito last teach?
Queens
Fun Fact: Ms. Brito used to teach in Brooklyn
A) A spinner is spun twice. Create a sample space list of ordered pairs that represent the outcomes of the spinner if it has 5 equal sectors.
B) Using your answer from A, determine the probability of obtaining two numbers with a sum of 5.
A) There are 25 outcomes.
(1,1) (2,1) (3,1) (4,1) (5,1)
(1,2) (2,2) (3,2) (4,2) (5,2)
(1,3) (2,3) (3,3) (4,3) (5,3)
(1,4) (2,4) (3,4) (4,4) (5,4)
(1,5) (2,5) (3,5) (4,5) (5,5)
B) 4/25
A) A four sided die is rolled three times, draw a tree-diagram that shows the sample space, S, of this experiement. How many elecemts are there?
B) What is the probability that you do not get 3 of the same number?
A) 64 elements
B) 1-4/64= 64/64-4/64
60/64
On a given day there is a 24% chance that it rains and a 17% chance that it snows. If there is a 6% chance that it will rain and snow on the same day, then what is the probability that it with either rain or snow?
=P(S)+P(R)-P(S and R)
=17+24-6
=35%
300 people have siblings. 150 of them have a brother, 75 of them have a sister, and 30 of them have both a brother and a sister. If one of them is drawn at random what is the probability that they have a brother if we know they have a sister?
.4 or 40%
How long has Ms. Brito been teaching?
14 years