1. Bellwork What fraction of the spinner is blue? Write in simplest form.
Suppose you spin. Are your chances of landing on a blue space the same as landing on a red space? Support your answer.
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?

2. Bellwork - ANSWERS
What fraction of the spinner is blue? Write in simplest form.
3/12 = ¼
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.

3. Bellwork – ANSWERS continued
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.

4. Cornell Notes with Summary
Probability
Cornell Notes with Summary
Essential Question: What is the difference between an outcome and an event and how are they related to probability?
NOTE TO TEACHERS: This slide includes the title for the notes, and the instructions regarding note-taking style. On subsequent pages, the slide title indicates the topic for the left-hand side of their Cornell Notes.

5. 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

6. 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)

7. 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
P (ace) = 4 aces = *always simplify*
52 cards
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.

8. 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
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.

9. total possible outcomes
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.

10. 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.

11. 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.

12. 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.

13. 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 = *in simplest form*
52 cards
P (spade) = 13 spades = *in simplest form*
52 cards
P (king or spade) = 1/ /4 = **common denominator needed** 4/ /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.
NOTE: you may want to discuss with students that simplifying at the *end,* instead of simplifying each event, is a better strategy when ADDING the probability of events with the same number of possible outcomes

14. 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?

15. HOMEWORK Find the probability of the following:
Drawing all spades from a deck of cards after 5 draws if you replace the cards each time.
Rolling a 4 or an odd number on a regular number cube.
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.

16. Exit Ticket Find P(3 or 5) on a number cube.
Susie rolls a regular number cube - is it likely, unlikely, or neither likely nor unlikely that she rolls an even number?
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?

17. Exit Ticket - ANSWERS
Find P(3 or 5) on a number cube. 1/6 + 1/6 = 2/6 = 1/3
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
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