Unit 2 Quiz 1 Practice Questions

Instructions: Classify each scenario as an example of simple, compound, or relative probability.

Groups:

(a) Simple Probability

,

(b) Compound Probability

,

(c) Relative Probability

• rolling 3 on a die and flipping tails on a coin

• selecting a female GIVEN that they wear Crocs in class

• drawing a seven of hearts from a full deck of cards

• selecting a male who wears Crocs FROM a class

Answer explanation

The Lesson 2 notes have anchor charts at the end related to the definitions for probabilities. Refer back to those. Explanations for two of the four options is listed below.

===== ===== ===== ===== =====

The male who wears Crocs FROM a class is an example of simple probability. This is because we are selecting something from the entire class. Simple probabilities select something from an entire group.

===== ===== ===== ===== =====

The female FROM those wearing Crocs is an example of relative probability. This is because we are selecting something from a subset of the class (not the entire class).

Researchers surveyed 100 students on what superpowers they would most like to have. What is the probability of wanting a power other than flying or invisibility FROM the females surveyed?

===== ===== ===== ===== =====
Instructions: Which options below describe the probability above? (Select two options)

• P(Other | Female)

• P(Flying or Invisibility | Female)

• P(Female | Other)

• 8/52

• 8/18

Answer explanation

What is the probability of wanting a power other than flying or invisibility FROM the females surveyed?

===== ===== ===== =====

P(Other | Females) = 8/52

===== ===== ===== =====

The word "FROM" helps. The event described after "FROM" belongs on the denominator (52 females). The event described before "FROM" belongs on the numerator (8 females wanted another power).

Researchers surveyed 100 students on what superpowers they would most like to have. What fractions represent the conditional probabilities shown?

Groups:

(a) P(Other | Female)

,

(b) P(Male | Fly)

,

(c) P(Fly | Male)

,

(d) P(Female | Other)

• 26/38

• 8/52

• 26/48

• 8/18

Answer explanation

The conditional probability notation helps you answer these questions. A fraction has to be calculated. Word problems let you know the denominator involves an event described after terms such as "FROM" and "GIVEN".

What is the probability of rolling a heads on a coin and then rolling an even number on a six-sided die?

Mathematical Equivalence

ON

Answer explanation

P(heads & even) = (1/2)(3/6) = 3/12

===== ===== ===== ===== =====

The answer can be rewritten in many ways:

3/12 = 1/4 = 0.25 = 25%

Which probability distributions are mathematically valid?

• 
• 
• 
• 

Answer explanation

There were two correct answers in this question. One of them is shown here. A valid distribution has a sum of 1 for all the shaded probabilities. There are two ways to interpret this rule.

===== ===== ===== ===== =====

Each shaded box represents 0.10 = 10%

If 10 boxes are shaded this is 1 = 100%

This image has 10 shaded boxes so it is valid

===== ===== ===== ===== =====

If you stack all the shaded boxes on top of each other they stop at 1

The distribution describes lotto ticket probabilities to win different amounts. What is the expected value for this lotto ticket? (Do not include a dollar symbol in answer)

Mathematical Equivalence

ON

Answer explanation

Expected Value is calculated by adding the product each paired outcome and probability

What is the connection between "expected value", "fair price", and profit from the gambler's perspective?

Groups:

(a) Expected Value (EV)

,

(b) Fair Price (FP)

,

(c) Profit

• money SPENT from gambling

• no profit if EV = FP

• price spent to gamble

• money WON from gambling

Answer explanation

Expected value (EV) = money won from gambling in the long-run; this is not related to one gambling event but instead a very large number of gambling events

===== ===== ===== ===== =====

Fair prices (FP) = money spent to gamble that in the long-run would result in no profit or lose from gambling

===== ===== ===== ===== =====

Profit = EV - Bet Price

No profit occurs when EV = Bet Price

This happens when bet price is the "fair price"