The probability of winning the lottery is 1/2; either you win or you don't
The probability someone gets a 5 on the AP Statistics test is .15. Mr. Otey teaches 17 students. Assume that all of his students' scores are independent, even though that is silly. What is the probability that all 17 of them get a 5?
What is (.15)^17 = ~0
You're very concerned about the possibility of spoiled milk at the milk and cookies party, so you're taste-testing all the milks. You know that 2% of the drinks are spoiled, and there are thousands of drinks, so you can treat each one as independent. What is the probability the first spoiled milk that you test is the 10th one?
Geometpdf (.02,1) = .0167
The class scores on a test are normally distributed, with an average of 78 and a standard deviation of 12 points. What is the probability that a randomly selected student got 70 or less?
What is .2525
I'm playing a game where I roll a fair dice. If it lands 6, I win $5. Otherwise, I lose $1. Find and interpret the expected value of my winnings from this game.
1/6(5)+5/6(-1) = 0. If I play this game many times, in the long run I would break even.
If I am rolling two fair dice, what is the probability that the sum of the two dice is 6?
What is 5/36 or 0.138
The probability John wears a green shirt is .05 each day, independently. What is the probability it will take him a month or less (assume 30 days) to wear a green shirt?
What is .7854
If X is a normal random variable with mean 0 and standard deviation 1, find the distribution of Y = 2X + 3.
Y is normally distributed with mean 3 and standard deviation 2.
A quarterback completes 44% of his passes, and each pass is independent. It is the beginning of football season, and he has not played any games yet. What is the probability that it takes him at least five passes to complete his first pass?
0.098
There are 7 boys and 10 girls in Stats. Mr. Otey is going to draw three popsicle sticks without replacement. What is the probability that at least one of them is a boy?
1-(10/17)*(9/16)*(8/15) =.823
No calculator allowed!
Geometpdf(.5,2)
This is the probability of getting your first success on the second trial when your probability of success is .5
=.5 * .5 = .25
Consider two independent random variables X and Y, both following a standard normal distribution. (I.e., N(0,1).)
Find the distribution of Z = aX + bY, where a and b are constants.
Z is normally distributed with mean 0 and standard deviation S
sqrt(a^2+b^2)
It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. Find the probability that the consumer buys exactly 4 contaminated chickens.
0.231
BTA's baseball team has a 70% chance of winning home games and 40% chance of winning away games. There's a 50% chance their next game is a home game, so what is the chance they win it?
What is .55
The probability Logan gets a hit is .15, for each at bat, independently. What is the probability it takes him at least 5 at bats to get a hit?
What is .5221
An average female is 5'4'' (64 inches) tall. The standard deviation for female heights is 2.5 inches. 21.19% of women are taller than Elena. Approximately how tall is she?
About 66 inches (5' 6")
An agent sells life insurance policies to five equally aged, healthy people. According to recent data, the probability of such an individual surviving for at least 30 years is 2/3. Calculate the probability that after 30 years at least three of the five people are still living.
1-binomialcdf(5,2/3,2) = 0.790
Mr. Otey is a 40% free throw shooter. What is the probability he makes exactly half of his next 10 shots?
What is .2007
The probability you will have a tire blowout on any given day is .015, independently. What is the probability you will have at least two blowouts in the next 100 days?
1-Binomcdf(100,.015,1) = .443
Freshman GPAs at Totally Real High School are normally distributed, with a mean of 2.93 and standard deviation of .39. What is the probability that a randomly selected group of 3 students has a total GPA of more than 9?
T = X1 + X2 + X3
T~N(8.79, .675)
P(T>9) = normalcdf(9,10000,8.79,.675) = .378
No calculator allowed!
Binomcdf(10,.7,10)
This is the probability that you get 10 or fewer successes on 10 trials, which is 1.