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Bellwork

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.

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Bellwork

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  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. Probability Cornell Notes with Summary Essential Question: Compare and contrast an outcome and an event and their relationship to probability.

  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) when events are mutually exclusive • The probability of one event AND / THEN another is found by multiplyingthe 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 P(B) • Dependent = P(A) x P(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 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.

  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 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 = 4/204 = 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. 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 = 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.

  14. Summary • Answer the Essential Question in two or more complete sentences. • EQ: Compare and contrast an outcome and an event and their relationship 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

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