Unit 7 Probability Notes

Open Ended

What is the Multiplication Rule for Counting and how does it help in solving problems involving large numbers of objects?

Open Ended

How many cards are there in a standard deck?

Multiple Select

Which of the following are learning objectives for the topic of permutations?

• Use the Multiplication Rule for Counting to determine the number of permutations.

• Compute expressions containing factorials.

• Compute permutations.

• Apply permutations to solve problems.

Fill in the Blank

A permutation is an ordered list of objects taken from a given population. The length of the list is given, and the list cannot contain any ___ items.

Open Ended

How many different podium placements (first place, second place, and third place) are possible in the final heat of Olympic swimming events featuring eight swimmers?

Multiple Choice

For any positive whole number n, the factorial of n (denoted n!) is the product of every whole number less than or equal to n. What is the value of 0!?

• 0

• 1

• n

• Infinity

Multiple Choice

What is the value of 8! divided by 6!?

• 56

• 720

• 40,320

• 24

Multiple Choice

Which of the following formulas represents the number of permutations of n objects taken r at a time?

• n!/(n-r)!

• n!/r!

• (n+r)!/n!

• n!/(n+r)!

Open Ended

Explain how factorials are used in the calculation of permutations.

Fill in the Blank

Find the number of permutations of 12 objects taken 3 at a time.

Multiple Choice

Which of the following statements is true about combinations?

• Order does not matter in combinations.

• Order matters in combinations.

• Combinations are the same as permutations.

• Combinations cannot be used for lists.

Open Ended

Distinguish between a permutation and a combination using a real-life example.

Multiple Choice

What is the formula for calculating the number of combinations of n objects taken r at a time?

• n!/(n-r)!

• n!/(r!(n-r)!)

• r!/(n!(n-r)!)

• n!/(r!r!)

Fill in the Blank

Compute the value of 8C3 using the combinations formula.

Open Ended

Explain the difference between single stage and multi-stage experiments in probability.

Multiple Choice

Which of the following best describes the sample space for flipping a coin ten times and counting the number of heads?

• {H, T}

• {0, 1, 2, ..., 10}

• {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

• {Heads, Tails}

Multiple Choice

List two criteria that must be met for tables to be useful in finding the sample space for multi-stage experiments.

• The experiment must have only two stages and the outcomes of each stage must have no effect on the outcomes of the other.

• The experiment must have more than two stages and the outcomes of each stage must affect the outcomes of the other.

• The experiment must have only one stage and the outcomes must be random.

• The experiment must have dependent stages and outcomes must be identical.

Fill in the Blank

The stages of a multi-stage experiment are called ___ if the outcome of one stage does not affect the outcome of the other.

Multiple Choice

What does it mean for two stages of an experiment to be independent?

• The outcome of one stage affects the other

• The outcome of one stage does not affect the other

• Both stages must have the same outcome

• Both stages must have different outcomes

Multiple Choice

Which of the following statements about probability is correct?

• Probability is always greater than 1

• Probability can be negative

• Probability is always between 0 and 1

• Probability is always equal to 0

Open Ended

Define probability and explain the difference between impossible and certain events.

Fill in the Blank

The probability of rolling a 7 with a standard six-sided die is ___.

Multiple Choice

Which formula represents the theoretical probability of an event E?

• P(E) = n(S)/n(E)

• P(E) = n(E)/n(S)

• P(E) = n(E) + n(S)

• P(E) = n(E) - n(S)

Multiple Choice

A standard deck of cards has 52 cards. What is the probability of drawing the 10 of spades from a well-shuffled deck?

• 1/13

• 1/26

• 1/52

• 1/10