Bellwork

1. What fraction of the spinner is blue? Write in simplest form.

2. Suppose you spin. Are your chances of landing on a blue space the same as landing on a red space? Support your answer.

3. Suppose you spin it twice. If the first time you land on a green space, does it impact your chances of landing on a green space the second time?

Bellwork - ANSWERS1. What fraction of the spinner is

blue? Write in simplest form.3/12 = ¼

2. If you spin the spinner, are your chances of landing on a blue space the same as landing on a red space? Support your answer.

No. There are only 3 blue spaces, while there are 5 red spaces. The chances of landing on blue are 3 out of 12, while the chances of landing on red are 5 out of 12. Therefore, the chances of landing on a red space are greater than landing on a blue space.

Bellwork – ANSWERS continued3. Suppose you spin it twice. If the

first time you land on a green space, does it impact your chances of landing on a green space the second time? Support your answer.

No. The number of green spaces and total spaces does not change from the first spin to the second – these events are independent from one another. Therefore the chances of landing on a green space the second time are the same as the first time.

Probability

Cornell Notes with Summary

Essential Question: What is the difference between an outcome and an event and how are they

related to probability?

Events

• Probability – the chance of an event happening expressed as a ratio with a value between 0 and 1.– What is the probability of rolling a 4 on a

regular number cube?• Since there is only 1 four, and 6 sides, the

probability is 1 out of 6, or 1/6

• The probability of rolling a 4 expressed as a decimal is .17

• Outcome – any possible result of an action

Multiple Events

– The probability of one event OR another is found by adding the probability of the first to the second

• P(A or B) = P(A) + P(B)

– The probability of one event AND / THEN another is found by multiplying the probability of the first to the second (making adjustments if they are dependent events)

• P(A and B) or P(A then B) – Independent = P(A x B)

– Dependent = P(A x B following A)

You Try It!

• Find the probability of choosing a spade from a deck of

cards, replacing it, AND then choosing an ace as the

second card.

• P (spade) = 13 spades = 1 *always simplify*

52 cards 4

• P (ace) = 4 aces = 1 *always simplify*

52 cards 13

• P (spade and ace) = 1/4 x 1/13 = 1/52

• The probability of choosing a spade from a deck of cards,

replacing it, and then choosing an ace as the second card is 1

out of 52.

You Try It!

• Find the probability of choosing a king from a deck of cards,

*not* replacing it, AND then choosing a jack as the second card.

• P (king on first pick) = 4 kings = 1 *always simplify*

52 cards 4

• P (jack given king on first pick) = 4 jacks *in simplest form*

51 cards

Remember, you kept the card from the first pick, so now there

are only 51 cards left in the deck.

• P (king, and then jack) = 1/4 x 4/51 = 1/51

• The probability of choosing a king from a deck of cards, not replacing

it, and then choosing a jack as the second card is 1 out of 51.

Likelihood of Events

• Everything has probability, but not everything is likely.

• Probability is represented as a ratio of:desired outcome

total possible outcomes

• Likelihood is where that probability lies between 0 and 1, where 0 is unlikely and 1 is likely.

Likelihood of Events - Likely

• If something is LIKELY, then the probability of it happening is closer to 1.– The probability of landing on a blue space on

a spinner with 5 spaces with 1 red space, 1 yellow space, and 3 blue spaces is 3/5,

therefore landing on a blue space is likely.

Likelihood of Events – Unlikely

• If something is UNLIKELY, then the probability of it happening is closer to 0.– The probability of rolling a 3 on a regular

number cube is 1/6, therefore rolling a 3 on a

regular number cube is unlikely.

Likelihood of Events – Neither

• If something has a 50/50 chance of happening, it is NEITHER likely nor unlikely. – For instance, the probability of tossing a head

or a tail on a coin is ½ for heads and ½ for tails. Therefore, tossing heads is neither likely nor unlikely.

You Try It!

• Find the probability of choosing a king from a deck of cards OR

choosing a spade. State if it is a likely, unlikely, or neither likely nor

unlikely event.

• P (king) = 4 kings = 1 *in simplest form*

52 cards 13

• P (spade) = 13 spades = 1 *in simplest form*

52 cards 4

• P (king or spade) = 1/13 + 1/4 = **common denominator needed** 4/52 + 13/52 = 17/52

• The probability of choosing a king or spade from a deck of cards is 17 out of

52 for one draw; therefore, it is UNLIKELY that you will choose a king or

spade.

Summary

• Answer the Essential Question in two or more complete sentences.

• EQ: What is the difference between an outcome and an event and how are they related to probability?

HOMEWORK

• Find the probability of the following:1. Drawing all spades from a deck of cards after

5 draws if you replace the cards each time.

2. Rolling a 4 or an odd number on a regular number cube.

3. Drawing all jacks from a deck of cards and not 5 on a regular number cube.

• Then, state whether each is likely, unlikely, or neither likely nor unlikely to occur.

Exit Ticket

1. Find P(3 or 5) on a number cube.

2. Susie rolls a regular number cube - is it

likely, unlikely, or neither likely nor unlikely

that she rolls an even number?

3. Bob draws a card from a deck, keeps the

card, and then draws another - is it likely,

unlikely, or neither likely nor unlikely that he

draws a spade and a 7?

Exit Ticket - ANSWERS

1. Find P(3 or 5) on a number cube. 1/6 + 1/6 = 2/6 = 1/3

2. Susie rolls a regular number cube - is it likely, unlikely, or

neither likely nor unlikely that she rolls an even number?

neither likely nor unlikely since the probability of rolling an

even number is 3/6 = 1/2

3. Bob draws a card from a deck, keeps the card, and then draws

another - is it likely, unlikely, or neither likely nor unlikely that

he draws a spade and a 7? the probability of drawing a

spade is 13/52 and the probability of drawing a seven is

4/51 (he kept the card after the first draw). Multiplying the

fractions, we end up with a probability of 52/2652 (or 1/52 if

simplified), which is an unlikely result