Basic Probability
We have a fair six sided die. What is the probability you roll a prime number?
Prime number are 2,3,5
3/6=0.50
What is the formula for probability?
Probability= Possible Outcomes/Total Outcomes
What are the two possible outcomes for a Binomial Distrubution?
A success or a failure
What is a random variable?
A variable whose value is unknown or a function that assigns values to each of an experiment's outcomes.
How do you prove two outcomes Independent?
P(A and B)= P(A) * P(B)
We have a four colored spinner. (Red, Blue, Green, Yellow) What is the probability of spinning green three times in a row.
Solving:
1/4 * 1/4 * 1/4= 0.0156
Between what two numbers will a probability value fall between?
0-1
What is the probability of getting exactly 4 successes in 8 independent trails, giving their is a success rate of .35
binormpdf( 8, .35, 4)= 0.1875
Define A= B+C
Find Mean of A
Mean of B=7.3
Mean of C= 2.5
Standard Deviation B= 2.03
Standard Deviation C: 0.741
Mean of A: 7.3 + 2.5= 9.8
Select Correct Answer
What Diagram is commonly used to solve for Independent Probabilities?
A. Triangle Diagram
B. Tree Diagram
C. Boxplot Diagram
D. Independce Diagram
Answer: B
If we select one card out of a 52 card deck what is the probability that that card is a face card and a club.
*Don't include aces as a face card!!
Solving:
3/52=0.058
What is the correct formula for the complement rule?
A.P(AC)=1 - P(A-C)
B.P(AC)=1 - P(A+C)
C. P(A)=1 - P(AC)
D. P(AC)= 1 - P(A)
Answer: D
What are the four binomial settings?
B: Binary
I: Independent
N: Number
S: Succes
Define A as A= B+C
Find Standard deviation of A
Mean of B=7.3
Mean of C= 2.5
Standard Deviation B= 2.03
Standard Deviation C: 0.741
Standard Deviation of A=
(2.03)^2 + (.741)^2= 4.67
Square root of 4.67= 2.161
The probability that you flip a coin on heads if you have a .5, where each coin flip is independent. You can flip the coin 3 times.
What is the probabilty that you flip the coin on heads at least once?
0.125
There are 6 blue marbles, 3 red marbles, and 5 yellow marbles in a bag. What is the probability of selecting a blue and red marble on the first two draws?
Solving:
9/14 * 8/13=.3956
What is the formula for the multiplication rule for probability?
P(A and B)= P(A) * P(B)
An AP Stats quick check has 10 multiple choice questions with four choice for each question. If you randomly quess on every question, what is the probability you get exactly 5 correct.
binormpdf(10, 0.25, 5)= 0.0584
Define A as A= B+C
Find Mean of A
xB| 1 , 2 , 3
pB| .23, .43, .34
xC| 1 , 2 , 3
p2| .33, .18, .49
Mean of B= 2.11
Mean of C= 2.16
Mean of A= 4.27
The probability that roll a dice and it be either a 1 or 2. You can you can roll the dice 4 time, each roll is independent.
What is the probabilty that you roll a 1 or 2 twice?
Answer: 0.0123
In a lottery game, there are 2 winners for every 100 tickets sold on average. If a man buys 10 tickets, what is the probability that he is a winner?
Solving
49/50^10=0.8171
1-0.8171=0.1829
What is the formula for the addition rule for probability?
P( A or B) = P(A) + P(B) - P( A and B)
A online store finds that 5% of people click on their advertisement every time it appears. Let C be the number of times the ad gets the first person to click on it. Assume ever click is independent.
Find the probability that a person first clicks on the ad the 7th time it appears.
geometpdf(.05, 7)= 0.0368
Define A as A= B+C
Find Standard deviation of A
xB| 1 , 2 , 3
pB| .23, .43, .34
xC| 1 , 2 , 3
pC| .33, .18, .49
Standard Deviation of XB= 0.7469
Standard Deviation of XC= 0.8913
Standard Deviation of A=
(0.7469)^2+(0.8913)^2= 1.3523
Square Root of 1.2608=1.1629
You have a four sectioned spinner with four equal sides, each spin is independent. You spin the spinner 5 times
What is the probabilty that you will spin a 3 on the second spin?
Answer: 0.0156