6.1: Discrete vs Continuous and Probability Tables
The main difference between a discrete and continuous random variable
What is there are gaps between acceptable values in discrete random variables
The probability that a 3 year old battery works is .7 and a graphing calculator requires 4 batteries to work. Ms. Coleman finds 4 batteries that are 3 years old in the back of her closet. What is the probability that she puts them in a calculator and it works?
WRITE THE EXPRESSION
4C4(0.7)4(0.3)0=.2401
You toss a fair coin 7 times. You want to know the probability of more than 4 tails. Check BINS
PASSES:
B: success=tails fail=not tails
I: Each coin flip unrelated to last
N: n=7
S: p=0.5
When rolling a die, there is a 1/6 chance of getting a 5. You roll a die 12 times hoping for a five each time. What is the expected number of fives? Also interpret this value
mean=expected value=np=1/6*12=2 times
In many, many rolls of twelve dice, the average number of fives rolled is 2.
This is one member of The Beatles
In a discrete random variable "Number of bedrooms in my home," the probability distribution looks like this:
X 1 2 3 4 5
P(X) 0.03 0.15 0.5 0.25 ?
Complete the data for P(5)
What is 1-(0.05+0.15+0.5+0.25)=0.07
The probability that a telemarketing employee reaches a live person is .11. Suppose they call 20 people in a night. What is the probability that they reach at least 5 people?
WRITE THE GRAPHING CALC WORK
binomialdist(n=20,p=0.11)
P(x≥ 5)=.061
When playing a mini game testing math skills that has 25 questions, you will "level up" and get harder questions when you get 2 right, and will drop back down to easier questions when you get 2 wrong. You want to know the probability you will get 10 questions right. Check BINS
FAIL
B: success=correct; fail=wrong
I: FAIL probability of success goes down if you get two right in a row
N: n=25
S: FAIL less likely to answer correctly if you are getting them right (qs get harder)
When rolling a die, there is a 1/6 chance of getting a 5. You roll a die 12 times hoping for a five each time. What is the standard deviation for the number of fives? Also interpret this value.
stdev=sqrt(np(1-p))=sqrt(12(1/6)(5/6))=1.29
In many, many rolls of 12 dice, the number of fives typically varies from the mean by about 1.29 fives.
This movie made the most money in the USA box office in 2025
What is A Minecraft Movie ~$423.9 million
The following are questions you might have to complete on a patient intake form. Label each of the following as discrete or continuous:
-heart rate in beats per minute
-temperature
-number of pregnancies you have had
-how many alcoholic drinks you have per week
-heart rate in beats per minute: Continuous
-temperature: Continuous
-number of pregnancies you have had: Discrete
-how many alcoholic drinks you have per week: Discrete
nC5(p)5(0.71)8
What is n? What is P?
n = 13 p = .29
In a large clinical trial of a vaccine for the flu, 8% developed the flu. You sample 20 random participants, and want to know the probability one or fewer of those sampled developed the flu. Check BINS
B: success-developed flu fail=no flu
I: randomly selected, unrelated participants
N: n=20
S: p=0.08
In a discrete random variable "Number of couches in my house," the probability distribution looks like this:
X 1 2 3 4 5
P(X) 0.2 0.2 0.31 0.14 0.15
What is the mean? Interpret it as well!
1(0.2)+2(0.2)+3(0.32)+4(0.14)+5(0.15)=2.87
In many, many houses, the average number of couches is 2.87.
This is the title of the first book in J.R.R. Tolkien’s The Lord Of The Rings trilogy?
What is The Fellowship Of The Ring?
In a discrete random variable "Number of couches in my house," the probability distribution looks like this:
X 1 2 3 4 5
P(X) 0.2 0.2 0.31 0.14 0.15
What is the probability a randomly selected person has at least 2 couches?
What is 0.8
It is estimated that 10% of drivers turn on their blinker before changing lanes. In a random sample of 4 drivers, what is the probability that at least one person uses his or her blinker when changing lanes?
WRITE THE GRAPHING CALC WORK
binomialdist(n=4,p=0.1)
P(x≥ 1)=.3439
Baldness at birth is an inherited trait which about 65% of people have. At a hospital in Sweden, 100 babies were born last week, all unrelated singlets (no twins, etc.). You want to determine the probability that more than 9 babies were born bald at that hospital. Check BINS.
FAILS
B: success=bald; fail=not bald
I: Each baby is unrelated
N: n=100
S: FAIL this is an inherited trait, some are more likely than others to have it.
In a discrete random variable "Number of couches in my house," the probability distribution looks like this:
X 1 2 3 4 5
P(X) 0.2 0.2 0.31 0.14 0.15
What is the standard deviation? Interpret it as well!
stdev=1.309 from the stapplet "Discrete Random Variables"
In many, many homes, the number of couches varies from the mean by about 1.309 couches.
How many teams are in the MLB
What is 30?
In a discrete random variable "Number of couches in my house," the probability distribution looks like this:
X 1 2 3 4 5
P(X) 0.2 0.2 0.31 0.14 0.15
Create a histogram for these data
See board
According to government data, 20% of employed women have never been married. 25 employed women are selected at random. Find the probability that the number of employed women who have never been married is greater than 3.
WRITE THE GRAPHING CALC WORK
binomialdist(n=25,p=0.2)
P(x≥ 4)=0.766
In a school-wide tournament you will play Rock, Paper, Scissors until you lose for the first time (you continue playing if it's a draw). Assume your challengers are randomly selected from the school and whether they will throw rock, paper, or scissors is also random. You want to know the probability you will still be playing in 10 rounds. Check BINS to determine if this is binomial.
FAILS
B: success=win or draw; fail=lose
I: assume you player is independent of the others
N: FAIL, no set number of trials
S: p=6/9=2/3
Create a probability distribution table for the discrete random variable "number of tails when a fair coin is flipped three times" then calculate and interpret it's mean.
X 0 1 2 3
P(X) 1/8 3/8 3/8 1/8
mean=0(1/8)+1(3/8)+2(3/8)+3(1/8)=1.5
In many, many flips of three coins, the average number of tails is 1.5
One of the seven ancient wonders of the world, a temple to this Greek goddess was located in Ephesus in what is modern day Turkey (Ms. Coleman has been there and seen the ruins)!
Who is Artemis?