Unit 3 Milestone – Concepts of Probability | 2026 Verified Answers & Solutions

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UNIT 3 MILESTONE on Concepts of Probability
26/27 that's 96%


26 questions were answered correctly.
1 question was answered incorrectly.


1. The average number of road accidents that occur on a particular stretch of road during
a month is 7.


What is the probability of observing exactly three accidents on this stretch of road next
month?
 0.023
 0.020
 0.052
 0.048
RATIONALE
Since we are finding the probability of a given number of events happening in a fixed
interval when the events occur independently and the average rate of occurrence is
known, we can use the following Poisson distribution formula:




The variable k is the given number of occurrences, which in this case, is 3 accidents.
The variable λ is the average rate of event occurrences, which in this case, is 7 accidents.




CONCEPT
Poisson Distribution




2.


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Using this Venn diagram, what is the probability that event A or event B occurs?
 0.42
 0.60
 0.22
 0.78
RATIONALE
To find the probability that event A or event B occurs, we can use the following formula
for overlapping events:



The probability of event A is ALL of circle A, or 0.39 + 0.18 = 0.57.
The probability of event B is ALL of circle B, or 0.21 + 0.18 = 0.39.
The probability of event A and B is the intersection of the Venn diagram, or 0.18.


We can also simply add up all the parts = 0.39 + 0.18 + 0.21 = 0.78.
CONCEPT
"Either/Or" Probability with Venn Diagrams and Two-Way Tables


3. What is the probability of NOT rolling a four when rolling a six sided die?
 5/6
 2/3
 1/6
 1/2
RATIONALE
Recall that the probability of a complement, or the probability of something NOT
happening, can be calculated by finding the probability of that event happening, and
then subtracting from 1. Note that the probability of rolling a four would be 1/6. So the
probability of NOT rolling a four is equivalent to:




CONCEPT
Complement of an Event



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4. Mark looked at the statistics for his favorite baseball player, Jose Bautista. Mark looked
at seasons when Bautista played 100 or more games and found that Bautista's
probability of hitting a home run in a game is 0.173.
If Mark uses the normal approximation of the binomial distribution, what will be the
variance of the number of home runs Bautista is projected to hit in 100 games? Answer
choices are rounded to the tenths place.
 3.8
 14.3
 0.8
 17.3
RATIONALE
In this situation, we know:
n = sample size = 100
p = success probability = 0.173
We can also say that q, or the complement of p, equals:
q = 1 - p = 1 - 0.173 = 0.827


The variance is equivalent to n*p*q:
CONCEPT
Normal Distribution Approximation of the Binomial Distribution


5. Maria flipped a coin 60 times, and the coin came up tails 32 times.
What is the relative frequency of the coin turning up heads in this experiment? Answer
choices are rounded to the hundredths place.
 0.53
 1.88
 2.14
 0.47
RATIONALE
Recall that, of the 60 flips, there are 32 tails. This means the remaining are heads, or 60-
32 = 28 heads. The relative frequency of a head is:




CONCEPT



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