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?

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.

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.

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.

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.

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.

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. 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

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: 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.

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?

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