Counting
Why is counting important?
I have 3 different suits, 4 different shirts and 6 different ties. How many different outfits do I have?
A person has 5 children. A child can be a G or a B. How many different outcomes are there?
Use the Permutations function to find how many ways there are to select 3 numbers of 10 (order matters. Drawing 1,2,3 is not the same as 2,1,3).
20 people are on a committee. A person needs to be selected to be chair, vice chair, and recorder. How many possibilities are there?
You’re creating a music CD of 10 songs. How many ways are there to arrange those songs?
A person has 5 children. How many different outcomes are there where there are 3 G’s? List them:
An urn has 5 balls numbered 1 through 5. You shall pull out 3 balls (without replacement) and put them in numerical order. How many outcomes are there? List them:
Use the calculator’s Combination Function to determine the number of ways of picking 3 out 5 (Combination means order doesn’t matter).
Using two answers above, what is the probability of having 5 children where 3 of them are G’s.
Binomial – use calculator’s binompdf function to answer the following: Format of binompdf(n,p,x)
There are 10 trials (n). Probability of “success” is .7 (p). What is the probability of exactly 7 successes (x)?
A basketball player makes 70% of his free throws. In a typical game, the player will shoot 10 free throws. What is the probability of making 5 of them?
If a person has 5 children, what is the probability of having 3 girls? What is the n, p, and x?
What will the binomcdf give us?
Poisson – use the calculator’s poissonpdf to answer the following questions: Format of poissonpdf(λt,x)
The rate is 5 per interval (λ). The number of intervals is 2. What is the probability of exactly 7 occurances (x)?
During a normal rainfall, the rate of drops is 8 drops per square foot in 10 minutes. What is the probability of 30 raindrops falling in 4 square feet in 10 minutes?
Customers normally enter a store at 5 per every 15 minutes. What is the probability of 0 customers entering in 15 minutes?
What is the complement and probability of complement to the previous question?
Customers normally enter a store at 5 per every 15 minutes. What is the probability of exactly 1 customers entering in a 5 minute period?
What will the poissoncdf give us?
Normal – use the calculators normalcdf to answer the following questions: Format of normalcdf(LB,UB,μ,σ)
With mean of 0, and StdDev of 1, what is the probability of getting a result between -1 and 1?
The height of men has a mean of 69 inches with a standard dev of 2 inches (not actual rates). What’s the probability of man being between 72 and 75 inches tall?
Stocks have an annual return of 8% with a standard deviation of 16%. What is the probability of having a return above 20% (technically, the UB is infinity. But a really big number will work perfectly, so let the UB be 1x1099. This is entered using the EE button.)
What is the probability of stocks having a return of less than 0? (The LB has to be a really big negative number. Use -1x1099)
Cabrillo Students (made-up data)
Number of Students: / Age:25 or under / Over
25
Transfer Program / 6,482 / 2,188
CTE (Voc Ed) Program / 1,955 / 4,043
Lifelong-Learning / 270 / 2,596
If a Cabrillo student is selected at random, what is the probability that the student selected is:
In the Transfer Program?
A Lifelong-learner?
Young (age 25 or younger) or in the Transfer Program?
Lifelong-Learner and is younger?
Older?
In Compound question, always think about breaking them down into more simple events.
Use both the probability & rules method and the counting method.
Poker, Texas Hold’em.
In Texas Hold’em you’re dealt two cards. Does order matter?
What is probability of being dealt:
“Pocket rockets”, two aces?
2 kings?
Probability of being dealt any pair?
Probability of being dealt “big slick”, an ace and a king?
Probability of being dealt AA, KK, or AK?
Probability of being dealt “suited big slick” (the ace and king are of the same suit)?
MP3 Player. My MP3 player has 42 Jimmy Buffett songs, 37 Eliane Elias songs, 19 Marcus Roberts songs, and 12 songs by other artists. The MP3 player is set so that songs are selected at random to be played without replacement. I will listen to only three songs.
How many different 3 song choices are possible if order matters?
How many different 3 song choices are possible if order doesn’t matter?
What is the probability of the first song being a JB?
What is the probability of the first two songs being a JB?
What is the probability that all 3 songs are by JB?
Probability of the three songs, IN ORDER, are by JB, followed by EE, followed by MR?
Probability that one song each of JB, EE, and MR is played, in any order?
Probability of Jimmy Buffet’s “Cheese Burger in Paradise” song is played first?
Probability “Cheeseburger in Paradise” is played at all (any of the first three)?
Probability that exactly one song by other artists is played?
Probability that at least one song by other artists is played?