Geo Semester B Unit 6 Notes

Multiple Choice

What is the volume of the prism given?

• $$72\ cm^3$$

• $$144\ cm^3$$

• $$288\ cm^3$$

• $$432\ cm^3$$

Multiple Choice

What is the volume of the cylinder given?

• $$62.8\ cm^2$$

• $$62.8\ cm^3$$

• $$125.6\ cm^3$$

• $$125.6\ in^3$$

Multiple Choice

What is the volume of the pyramid?

• $$432\ cm^2$$  

• $$144\ cm^2$$  

• $$432\ cm^3$$  

• $$144\ cm^3$$  

Multiple Choice

What is the volume of a rectangular pyramid with the dimension of the base 5 in x 3 in, and height 8 in?

• $$20\ in^3$$

• $$40\ in^3$$

• $$80\ in^3$$

• $$120\ in^3$$

Multiple Choice

What is the volume of the cone?

• $$103.62\ cm^3$$

• $$310.86\ cm^3$$

• $$932.58\ cm^3$$

• $$932.58\ in^3$$

Multiple Choice

What is the volume of the cone?

• $$103.62\ cm^3$$

• $$310.86\ cm^3$$

• $$932.58\ cm^3$$

• $$932.58\ in^3$$

Multiple Choice

What is the volume of the sphere?

• $$100.2\ cm^3$$

• $$276.55\ cm^3$$

• $$267.95\ cm^3$$

• $$803.84\ cm^3$$

Multiple Choice

What is the volume of the sphere with a diameter of 15 m?

• $$1592.55\ m^3$$

• $$1766.25\ m^3$$

• $$5295.75\ m^3$$

• $$6005.75\ m^3$$

Do the two stacks of coins have the same volume? How do you know?

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Since the 2 stacks have the same kind and amount of coins, it makes sense to say that the two stacks have the same volume. The arrangement of the coins does not effect the volume. This is Cavelieri's Principle. The coins have the same cross-sectional area (same coin) at every plane parallel to the base.

Compare the volume of the stacks of coins.

• Some of the coins are larger than the others. There is no easy way to tell whether the stacks have the same volume.

Independent and Dependent Events - Probability

Independent & Dependent Events

• Independent - One activity does not effect the outcome of a different activity. (Drawing marbles from a bag, but putting them back each time.)

• Dependent - One activity DOES effect the outcome of another activity. (Drawing a card from a deck of cards, not putting it back and drawing another.)

Multiple Select

You roll a number cube twice. The first time is a 3 and the second time is an even number.

• Independent

• Dependent

Multiple Select

You randomly draw a marble from a bag of marbles. You get a red and don't put it back into the bag. You draw another marble out of the bag and get a yellow.

• Independent

• Dependent

Probability of an Independent Event

Use the formula for the probability of independent events.

P(A and B) = P(A)⋅P(B)

Example: Find the probability of spinning an odd number on a spinner numbered 1 - 5; and the probability of flipping a coin and landing on tails.

Probability of an Independent Event

Use the formula for the probability of independent events.

P(A and B) = P(A)⋅P(B)

Example: Find the probability of spinning an odd number on a spinner numbered 1 - 5; and the probability of flipping a coin and landing on tails.

Multiple Choice

Find the probability of spinning a 2 on a spinner numbered 1 - 5; and the probability of flipping a coin and landing on tails.

• 1/10 or 10%

• 1/4 or 25%

• 1/2 or 50%

• 2/3 or 67%

Multiple Choice

People are randomly chosen to be game show contestants from an audience of 100 people. You are with 5 of your relatives and 6 other friends. What is the probability that you, your relatives, and your friends are not chosen to be either of the first two contestants?

• 50/70 or 71.4%

• 58/75 or 77.3%

• 60/70 or 85.7%

• 88/100 or 88%

Table Diagram

You roll a number cube and flip a coin. What is the probability of rolling a number greater than 4 and flipping tails? Use a table to find the sample space.

P(greater than 4 and tails)

Fill in the Blanks

What is the probability of rolling at most 4 and flipping heads?

Mutually Exclusive Events

When two events CANNOT happen at the same time, the events are said to be MUTUALLY EXCLUSIVE.

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An example of this is getting heads on a coin and a tail on the same coin in the same toss.

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Another example would be getting a six on a regular die and a five on the same die in the same roll.

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A pre-Covid example would be being at school and being at home at the same time.

Multiple Choice

If you are picking a card randomly from a deck of cards, the events of picking a jack and picking a heart are ...

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

If you are picking a card randomly from a deck of cards, the events of picking an ace and picking a ‘3’ are ...

• Mutually Exclusive

• Not Mutually Exclusive

If a set of mutually exclusive events covers all possible outcomes then their sum of probabilities is 1.

Example: Arif throws a biased coin. The probability of getting tails is 0.7. Therefore, the probability of getting heads is 1 - 0.7 = 0.3

Multiple Choice

Said throws a biased coin. The probability of getting tails is 0.4.

Work out the probability of getting heads.

• 0.4

• 0.6

• 0.8

• 0.2

More complicated OR

• To the right you see cards that can each be described in two ways

• Jack, Queen, King or Ace

• Heart, Club, Diamond or Spade

• So, one card can be two things at once, for example a Queen and a Heart.

When we talk about OR probabilities we have to take "double identity" into account.

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P(Queen or Heart) seems simple... just add the Queen probability to the Heart probability.... BUT

What about the Queen of Hearts? It will get counted twice, so....

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We will have to consider OR and take away AND to get rid of the double count

P(A or B) = P(A) + P(B) - P(A and B)

P(Queen OR Heart) = P(Queen) + P(Heart) - P(Queen of Hearts)

= 4/16 + 4/16 - 1/16

P(Queen or Heart) = 7/16

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​ In this simple example we can count the cards shown to see this is true!

Multiple Choice

If you draw one card from a standard deck, what is the probability of drawing a 5 or a diamond?

• 2/52
• 4/52
• 16/52
• 26/52

Multiple Choice

Which of the following shows how to determine P(shaded number or number less than five)?

• 4/8 + 4/8 - 2/8
• 4/9 + 2/8 - 4/8
• 4/8 + 6/8 + 2/8
• 2/8 + 4/8 - 4/8

Multiple Choice

If you roll one die, what is the probability of getting an even number or a multiple of 3?

(Looking at the picture might help you think about this)

• 1/3

• 2/3

• 1/2

• 1/6

Multiple Choice

If you roll one die, what is the probability of getting an even number or a multiple of 3?

(Looking at the picture might help you think about this)

• 1/3

• 2/3

• 1/2

• 1/6

Multiple Choice

The enrollment at Southburg High School is 1400. Suppose 550 students take French, 700 take algebra, and 400 take both French and algebra. What is the probability that a student selected randomly takes French or algebra?

Hint: P(French) + P(Algebra) - P(French and Algebra)

• 1250/1400

• 700/1400

• 550/1400

• 17/28