Sophia Statistics Unit 3
Milestone Complete 2021
Score 22/27
You passed this Milestone
22 questions were answered correctly.
UNIT 3 — MILESTONE 3
5 questions were answered incorrectly.
1
Which of the following is a property of binomial distributions?
The sum of the probabilities of successes and failures is always 1.
All trials are dependent.
The expected value is equal to the number of successes in the experiment.
There are exactly three possible outcomes for each trial.
RATIONALE
Recall that for any probability distribution, the sum of all the probabilities must sum to 1.
CONCEPT
Binomial Distribution
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2
Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing
a face card or an Ace.
,Choose the correct probability of drawing a face card or an Ace. Answer choices are in the form of a
percentage, rounded to the nearest whole number.
8%
4%
31%
25%
RATIONALE
Since the two events, drawing a face card and drawing an ace card, are non-overlapping, we can use the
following formula:
CONCEPT
"Either/Or" Probability for Non-Overlapping Events
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3
John is playing a game with a standard deck of playing cards. He wants to draw a jack on the first try.
Which of the following statements is true?
The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and
draws again, the probability that he will pull another jack increases.
The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and
draws again, the probability that he will pull another jack stays the same.
The probability that John draws a jack on the first try is 3/13. If John replaces the card, re-shuffles, and
draws again, the probability that he will pull another jack stays the same.
, The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and
draws again, the probability that he will pull another jack decreases.
RATIONALE
Events are said to be independent if one event does not influence the likelihood of the other. Since John re-
shuffles the deck and puts the card back in the deck, the probability should be the same and the first draw will
not influence the second.
CONCEPT
Independent vs. Dependent Events
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4
A magician asks an audience member to pick any number from 6 to 15.
What is the theoretical probability that an individual chooses the number the magician has in mind?
RATIONALE
If we suppose that the card chosen by the magician is fixed, then there are 10 possible values, {6, 7, 8, 9, 10, 11,
12, 13, 14, or 15}, that are all equally likely. So, the probability that a specific value is chosen is:
CONCEPT
Milestone Complete 2021
Score 22/27
You passed this Milestone
22 questions were answered correctly.
UNIT 3 — MILESTONE 3
5 questions were answered incorrectly.
1
Which of the following is a property of binomial distributions?
The sum of the probabilities of successes and failures is always 1.
All trials are dependent.
The expected value is equal to the number of successes in the experiment.
There are exactly three possible outcomes for each trial.
RATIONALE
Recall that for any probability distribution, the sum of all the probabilities must sum to 1.
CONCEPT
Binomial Distribution
I need help with this question
2
Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing
a face card or an Ace.
,Choose the correct probability of drawing a face card or an Ace. Answer choices are in the form of a
percentage, rounded to the nearest whole number.
8%
4%
31%
25%
RATIONALE
Since the two events, drawing a face card and drawing an ace card, are non-overlapping, we can use the
following formula:
CONCEPT
"Either/Or" Probability for Non-Overlapping Events
I need help with this question
3
John is playing a game with a standard deck of playing cards. He wants to draw a jack on the first try.
Which of the following statements is true?
The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and
draws again, the probability that he will pull another jack increases.
The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and
draws again, the probability that he will pull another jack stays the same.
The probability that John draws a jack on the first try is 3/13. If John replaces the card, re-shuffles, and
draws again, the probability that he will pull another jack stays the same.
, The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and
draws again, the probability that he will pull another jack decreases.
RATIONALE
Events are said to be independent if one event does not influence the likelihood of the other. Since John re-
shuffles the deck and puts the card back in the deck, the probability should be the same and the first draw will
not influence the second.
CONCEPT
Independent vs. Dependent Events
I need help with this question
4
A magician asks an audience member to pick any number from 6 to 15.
What is the theoretical probability that an individual chooses the number the magician has in mind?
RATIONALE
If we suppose that the card chosen by the magician is fixed, then there are 10 possible values, {6, 7, 8, 9, 10, 11,
12, 13, 14, or 15}, that are all equally likely. So, the probability that a specific value is chosen is:
CONCEPT
