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 13 students. Assume that all of his students' scores are independent, even though that is silly. What is the probability that all 13 of them get a 5?
What is (.15)^13 = ~0
The probability you find a defective bag of popcorn is .02, independently. What is the probability the first defective bag will be the 10th bag?
What is .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.
JJ is a 40% free throw shooter. What is the probability he makes exactly half of his next 10 shots?
What is .2007
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
No calculator allowed!
Binomcdf(10,.7,10)
This is the probability that you get 10 or fewer successes on 10 trials, which is 1.
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
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
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
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) = 1 - normalcdf(9,10000,8.79,.675) = .378
An agent sells life insurance policies to five equally aged, healthy people. According to recent data, the probability of a person living in these conditions for 30 years or more 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