STATISTICS MISC
UNIT 3 – MILESTONE 3
You passed this Milestone
Ryan is playing a multiplication game with a pile of 26 cards,
... [Show More] each with a number on them. Each turn, he flips over two of the cards, and has to multiply the numbers.
How many possible outcomes are there on Ryan's first turn flipping two cards?
676
26
650
52
RATIONALE
We can use the general counting principle and note that for each step, we simply multiply all the possibilities at each step to get the total number of outcomes. If we assume that the numbers are 1 - 26, then the overall number of outcomes is:
Note that once a number is chosen it cannot be chosen again. So the number of possible outcomes for the first card would be 26 since they could choose any card number 1 through 26. However, the second card chosen would only have 25 possible outcomes since the first card has already been drawn.
CONCEPT
Fundamental Counting Principle 2
What is the probability of NOT drawing a face card from a standard deck of 52 cards?
RATIONALE
Recall that the probability of a complement, or the probability of something NOT happening, can be calculated by finding the probability of the event happening, and then subtracting that from 1. Note that there are a total of 12 face cards in a standard deck of 52 cards. So the probability of NOT getting a face card is equivalent to:
CONCEPT
Complement of an Event 3
Using the Venn Diagram below, what is the conditional
probability of event B occurring, assuming event A has happened [P(B|A)]?
0.77
0.63
0.24
0.41
RATIONALE
To get the probability of B given A has occurred, we can use the following conditional formula:
The probability of A and B is the intersection, or overlap, of the Venn diagram, which is 0.41. The probability of A is all of Circle A, or 0.24 + 0.41 = 0.65.
CONCEPT
Conditional Probability 4
Annika was having fun playing poker. She needed the next two cards dealt to be diamonds so she could make a flush (five cards of the same suit). There are 15 cards left in the deck, and five are diamonds.
What is the probability that the two cards dealt to Annika (without replacement) will both be diamonds? Answer choices are in percentage format, rounded to the nearest whole number.
10%
29%
13%
33%
RATIONALE
If there are 15 cards left in the deck with 5 diamonds, the probability of being dealt 2 diamonds 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 diamond would be 5 out of 15, or . The probability that the second card is a diamond, given
that the first card was also a diamond, would be because we now have only 14 cards remaining and only 4 of those cards are diamond (since the first card was a diamond).
So we can use these probabilities to find the probability that the two cards will both be diamonds:
CONCEPT
"And" Probability for Dependent Events 5
Using this Venn diagram, what is the probability that event A or event B occurs?
0.77
0.36
0.68
0.41
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 0.24 + 0.41 = 0.65. The probability of event B is ALL of circle B, or 0.12 + 0.41 = 0.53.
The probability of event A and B is the intersection of the Venn diagram, or 0.41. We can also simply add up all the parts = 0.24 + 0.41 + 0.12 = 0.77.
CONCEPT
"Either/Or" Probability for Overlapping Events 6
Which of the following is an example of a false positive?
Sending a guilty man to jail.
A medical test coming back negative for a disease you don't have.
Sending an innocent man to jail.
A medical test coming back positive for a disease you do have.
RATIONALE
Sending a man to jail, when in fact he is innocent, is a false positive.
CONCEPT
False Positives/False Negatives 7
A bag contains 8 red marbles, 7 blue marbles, and 6 green marbles. Adam randomly picks out a marble from the bag.
What is the theoretical probability that Adam will pick a blue marble from the bag?
RATIONALE
Recall that there are 7 blue marbles and a total of 8+7+6 = 21 marbles overall. The probability of a blue is:
CONCEPT
Theoretical Probability/A Priori Method 8
Two sets A and B are shown in the Venn diagram below.
Which statement is TRUE?
Set A has 8 elements.
Sets A and B have 3 common elements.
There are a total of 2 elements shown in the Venn diagram.
Set B has 7 elements.
RATIONALE
The intersection, or middle section, would show the common elements, which is 3.
The number of elements of Set A is everything in Circle A, or 8+3 = 11 elements, not 8 elements. The number of elements of Set B is everything in Circle B, or 7+3 = 10 elements, not 7 elements.
To get the total number of items in the Venn diagram, we add up what is in A and B and outside, which is 8+3+7+2=20 elements, not 2 elements.
CONCEPT
Venn Diagrams 9
Kyle was trying to decide which type of soda to restock based on popularity: regular cola or diet cola. After studying the data, he noticed that he sold less diet cola on weekdays and weekends. However, after combing through his entire sales records, he actually sold more diet cola than regular cola.
Which paradox had Kyle encountered?
Benford's Law
Simpson's Paradox
False Negative
False Positive
RATIONALE
This is an example of Simpson's paradox, which is when the trend overall is not the same that is examined in smaller groups. Since the sale of diet coke overall is larger but this trend changes when looking at weekend/weekday, this is a reversal of the trend.
CONCEPT
Paradoxes 10
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.
4%
8%
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 11
A survey asked 1,000 people which magazine they preferred, given three choices. The table below breaks the votes down by magazine and age group.
Age Below 40 Age 40 and Above
The National Journal 104 200
Newsday 120 230
The Month 240 106
If a survey is selected at random, what is the probability that the person voted for "Newsday" and is also age 40 or older? Answer choices are rounded to the hundredths place.
0.34
0.23
0.54
0.66 [Show Less]