Sophia Statistics Unit 3 Milestone Complete

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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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.
Sophia Statistics Unit 3
Milestone Complete 2021
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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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 reshuffles
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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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
Theoretical Probability/A Priori Method
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Select the following statement that describes non-overlapping events.
Receiving the Queen of Diamonds fulfills Luke's need of getting both a face card and a diamond.
Luke wants a red card so he can have a winning hand, and he receives the five of clubs.
Luke needs to roll an odd number to win. When it’s his turn, he rolls a five.
To win, Luke needs a black card. He receives an eight of spades.
RATIONALE
Events are non-overlapping if the two events cannot both occur in a single trial of a chance experiment. Since
he wants a red card {Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, or King: In either Diamond or Hearts} and he got
the Five of Clubs, there is no overlap.
CONCEPT
Overlapping Events
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Jake tosses a coin and rolls a six-sided die.
All of the following are possible outcomes EXCEPT:
Tails, Three
Heads, Seven
Heads, Five
Tails, One
RATIONALE
Recall a coin has heads and tails and a standard die has six values, {1, 2, 3, 4, 5, or 6}. So, obtaining a value of
7 is not possible.
CONCEPT
Outcomes and Events
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Asmita went to a blackjack table at the casino. At the table, the dealer has just shuffled a standard deck of 52
cards.
Asmita has had good luck at blackjack in the past, and she actually got three blackjacks with Aces in a row the
last time she played. Because of this lucky run, Asmita thinks that Ace is the luckiest card.
The dealer deals the first card to her. In a split second, she can see that it is a non-face card, but she is unsure if it
is an Ace.
What is the probability of the card being an Ace, given that it is a non-face card? Answer choices are in a
percentage format, rounded to the nearest whole number.
8%
77%
69%
10%
RATIONALE
The probability of it being an Ace given it is a Non-face card uses the conditional formula:
Note, that in a standard deck of 52 cards, there are 12 face cards, so 40 non-face cards. Of those non-face cards,
there are only 4 Aces.
CONCEPT
Conditional Probability
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Patricia was having fun playing poker. She needed the next two cards dealt to be spades so she could make a
flush (five cards of the same suit). There are 12 cards left in the deck, and three are spades.
What is the probability that the two cards dealt to Patricia (without replacement) will both be spades?
Answer choices are in percentage format, rounded to the nearest whole number.
17%
18%
5%
25%
RATIONALE
If there are 12 cards left in the deck with 3 spades, the probability of being dealt 2 spades if they are dealt
without replacement means that we have dependent events because the outcome of the first card will affect the
probability of the second card. We can use the following formula:
The probability that the first card is a spade would be 3 out of 12, or . The probability that the second card is
a spade, given that the first card was also a spade, would be because we now have only 11 cards remaining
and only two of those cards are spades (since the first card was a spade).
So we can use these probabilities to find the probability that the two cards will both be spades:
CONCEPT
"And" Probability for Dependent Events
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