Unit 2 Quiz 1 Practice Questions v2

The picture represents a probability distribution for five different outcomes. Label both axes.

a

b

Outcomes

Probability

The picture represents a probability distribution for five different outcomes. Probabilities are represented from 0 to 1. The sum of all event probabilities must equal 1 for the probability distribution to be valid.

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The 0 represents ​ (a)   chance for an event to happen.

The 1 represents ​ (b)   chance for an event to happen.

This probability distribution needs ​ (c)   boxes to be shaded to be valid.

• 0%
• 100%
• 7
• 8
• 9
• 10
• 5

Answer explanation

The probability axis has 7 divisions from top to bottom. So 7 divisions need to be shaded for a valid distribution.

How many divisions need to be shaded for each probability distribution to be valid?

• 10

• 
• 8

• 
• 7

• 
• 9

• 

Answer explanation

Count the # of divisions along the probability axis from top to bottom. This tells you how many divisions need to be shaded for a valid distribution.

Which probability distributions are mathematically valid?

• 
• 
• 
• 

Answer explanation

Each image has 8 divisions from top to bottom. This means a valid probability distribution needs to have 8 shaded divisions. Only two of the images are valid.

Represent the probability distribution data on the table.

e

d

c

a

b

0.30

Cat

Rabbit

0.00

0.40

Answer explanation

This is a valid probability distribution for a lotto ticket with five different payout amounts. What is the expected value for the lotto ticket?

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(hint: each shaded region represents 0.10; do not include $ symbol in final answer)

Mathematical Equivalence

ON

Answer explanation

Count the shaded bocks to know the probability for each outcome. (example: $1 has four shaded blocks so its probability is 0.40; $5 has two shaded blocks so its probability is 0.20; continue this pattern to identify all the probabilities)

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I represented the data as a table. This step is not necessary but I wanted you to see this for your learning.

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Use the expected value equation. You find the sum of the ordered pairs of outcomes and probabilities. This shows the expected value is $11.40

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DIVING DEEPER

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Expected value = $11.40 (this is how much money you WIN on average for each ticket you buy)

Fair price = $11.40 (if you PAY this much for each ticket you buy, then on average you make no gambling profit)

Profit = 0 if your lotto ticket PRICE is the fair value (0 = 11.40 - 11.40)

Shoe data on 25 students from a class was collected. What sentences describe the following conditional probability notations?

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P(C | F) = probability someone wears ​ (a)   IF YOU KNOW they are ​ (b)  

P(N | M) = probability someone wears ​ (c)   IF YOU KNOW they are ​ (d)  

• Crocs
• female
• Nike
• male

Answer explanation

P(C | F) = probability someone wears Crocs IF YOU KNOW they are female

P(N | M) = probability someone wears Nike IF YOU KNOW they are male

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Conditional probability notation follows this pattern:

P(event | known event)

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With conditional probabilities, the event after the vertical line is known.

What fraction represents the conditional probability of P(C | F)? Do not convert your answer to a decimal. Just write the fraction.

Mathematical Equivalence

ON

Answer explanation

What fraction represents the conditional probability of P(C | F)?

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8 = # of Croc wearing female students

13 = # of female students

P(C | F) = 8/13

What conditional probability expression represents the fraction shown?

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P( ​ (a)   | ​ (b)   ) = 3/5

• M
• O
• F
• N
• C

Answer explanation

What conditional probability expression represents the fraction shown? (3/5)

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3 = P(M and O) = probability of male wearing another shoe brand

5 = P(O) = probability of wearing another shoe brand

3/5 = P(M | O) = probability of selecting a male IF YOU KNOW they wear another shoe brand

What is the probability of spinning green and rolling an even number? Represent your answer as a fraction.

Mathematical Equivalence

ON

Answer explanation