Introduction to statistics
MILESTONE 3 RETAKE GUIDE
Sophia Learning Center
Actual Questions & Verified Answers with Rationales
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, UNIT 3 — MILESTONE 3
23/27
23/27 that's 85% RETAKE
23 questions were answered correctly.
4 questions were answered incorrectly.
1
●
Ryan is playing a multiplication game with a pile of 26 cards, 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?
26
●
676
●
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
theUNIT
number3of— MILESTONE
possible outcomes for 3
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 23/27
since the first card has already been drawn.
CONCEPT
→ Fundamental Counting Principle
Report an issue with this question
2
●
Using this Venn diagram, what is the probability that event A or
event B occurs?
0.36
●
0.77
, UNIT
●
3 — MILESTONE 3
0.68
23/27
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 with Venn Diagrams and Two-Way
Tables
Report an issue with this question
3
●
Peter randomly draws a card from a deck of 24. The odds in favor of
his drawing a spade from the cards are 1:3.
What is the probability ratio for Peter to draw a spade?
●
●
MILESTONE 3 RETAKE GUIDE
Sophia Learning Center
Actual Questions & Verified Answers with Rationales
100% Guarantee Pass
, UNIT 3 — MILESTONE 3
23/27
23/27 that's 85% RETAKE
23 questions were answered correctly.
4 questions were answered incorrectly.
1
●
Ryan is playing a multiplication game with a pile of 26 cards, 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?
26
●
676
●
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
theUNIT
number3of— MILESTONE
possible outcomes for 3
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 23/27
since the first card has already been drawn.
CONCEPT
→ Fundamental Counting Principle
Report an issue with this question
2
●
Using this Venn diagram, what is the probability that event A or
event B occurs?
0.36
●
0.77
, UNIT
●
3 — MILESTONE 3
0.68
23/27
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 with Venn Diagrams and Two-Way
Tables
Report an issue with this question
3
●
Peter randomly draws a card from a deck of 24. The odds in favor of
his drawing a spade from the cards are 1:3.
What is the probability ratio for Peter to draw a spade?
●
●
