Formulas/Random
The probabilities of a probability distribution always sum to _
1
There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will snow exactly 2 days.
binompdf (n=25, p=.1, x=2)
There is a 10% chance of snow on a given day in December. Find the probability that the first day of snow is the 8th day you sample.
geompdf(p=.1, r=8)
x=2, p(x)=0.15
x=3, p(x)=0.25
x=4, p(x)=0.20
x=5, p(x)=0.30
x=6, p(x)=0.10
Find p(x<5)
p(x<5)=0.60
Find the missing percentage
x = 1, p(x)=0.49
x=2, p(x)=0.26
x=3, p(x)=0.07
x=4, p(x)=___
p(x)=0.18
There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will snow less than 4 days.
binomcdf (n=25, p=.1, x = 3)
There is a 10% chance of snow on a given day in December. Find the probability that the first day of snow is within the first 11 you sample.
geomcdf(p=.1, p=11)
x=2, p(x)=0.15
x=3, p(x)=0.25
x=4, p(x)=0.20
x=5, p(x)=0.30
x=6, p(x)=0.10
Find p(x=3 U x>5)
Find p(x=3 U x>5)=0.35
A pharmaceutical company produces a new vaccine that has a 90% chance of being effective.
Assume the outcomes for each patient are independent. The vaccine is given to 5 patients.
X=number of patients for whom the vaccine is effective
The Give all values of x.
x=0, x=1, x=2, x=3, x=4, x=5
There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will snow more than 4 days.
1 - binomcdf(n=25, p=.1, x=4)
There is a 10% chance of snow on a given day in December. Find the probability that you sample more than 15 days before you the first day of snow.
1-geomcdf(p=.1, p=15)
x=2, p(x)=0.15
x=3, p(x)=0.25
x=4, p(x)=0.20
x=5, p(x)=0.30
x=6, p(x)=0.10
Find p(x<4 and x>2)
p(x<4 and x>2)=0.25
A jar contains 5 green pens and 10 yellow pens.
A person randomly selects one pen at a time with replacement.
What is the probability that it takes the person 3 tries to pick their first green pen?
Write the formula.
Check the formula with Ms. Rubio
There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will snow at least of 5 days
1 - binomcdf(n=25, p=.1, x = 4)
There is a 15% chance of someone having red hair. What is the mean number of people you would need to sample to find the first person with red hair?
1/.15 = 6.67
x=2, p(x)=0.15
x=3, p(x)=0.25
x=4, p(x)=0.20
x=5, p(x)=0.30
x=6, p(x)=0.10
Find p(x is even | x>3)
p(x is even | x>3)=0.3/0.6=0.5
A jar of pens has 3 red pens, 4 blue pens, and 6 black pens. What is the probability of selecting 6 marbles with replacement and getting exactly 2 black pens?
Write the formula.
Check formula with Ms. Rubio
There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will snow at most 15 days.
binomcdf (n=25, p=.1, x= 15)
There is a 10% chance of snow on a given day in December. Find the probability that the first day of snow either the 7th or 9th day you sample.
geompdf(p=.1, r=7)+geompdf(p=.1, r=9)
A basketball player takes two free throws in a row.
The probability she makes the first shot is 0.6.
If she makes the first, the probability she makes the second is 0.7.
If she misses the first, the probability she makes the second is 0.4
Create a probability distribution.
Check with Ms. Rubio