Probability Probability Marbles Tiles OR add Always think
Probability
Probability •
Marbles •
Tiles •
OR - add • Always think about the possibility of an overlap. • Ex: If you are choosing one card from a deck, can it be a queen and a seven? • Ex: If you are choosing one card from a deck, can it be red and a jack? • If there is a possibility of an overlap, it needs to be subtracted!
Or - add • 1. You have 3 pencils, 6 erasers, 4 sharpies, and 7 pens. What is the probability of choosing a pencil or a pen? • 2. Marbles: 4 red, 5 green, 1 oranges, 12 yellow, 3 black What his the probability of choosing a red marble or a yellow marble? 3. Deck of cards: What is the probability of choosing a king or a diamond?
And - multiply • You are flipping a coin and rolling a die. What is the probability of flipping a “heads” and rolling a 3 or higher? • You are rolling a die and spinning a spinner from 1 -10. What is the probability of rolling an odd number and spinning a number less than 4?
Replacement “with replacement” – after you choose one, you put it back in and choose another “without replacement” – after you choose one, you do NOT put it back in before you choose another Ex: If there 20 names in a bag and I choose 1, how many names are now in the bag? ______ If I replace the name I chose, how many are now in the bag? _______
Names of 10 boys and 12 girls are placed in a hat. What is the probability of drawing a girl’s name, replacing it, and then drawing a boy’s name?
• Names of 20 boys and 16 girls are placed in a hat. What is the probability of drawing a boy’s name, not replacing it, and then drawing a girl’s name?
Marbles 14 red, 8 blue, 20 green, 3 black, 9 purple 1. What is the probability or drawing green, then purple (with replacement)? 2. What is the probability of drawing blue, then red (without replacement)?
Deck of Cards • Red: • Black: • Suits: • Cards:
• • 1. P(king) 2. P(heart) 3. P(king of hearts) 4. P(two) 5. P(heart and a four) with replacement 6. P(queen and a diamond) with replacement 7. P(ace or seven) 8. P(jack or club)
Classwork 5 red, 4 blue, 8 orange, 2 yellow, 3 brown 1. P(blue) 2. P(orange) 3. P(red or brown) 4. P(not yellow) 5. Probability of picking a red marble and then an orange marble, without replacement? • 6. Probability of picking a blue marble and then a yellow marble, with replacement? • 7. P(yellow or blue or red) • • •
Finding Odds against an event • Odds in favor of an event • What are the odds of the spinner landing on a number greater than or equal to 6? What are the odds in favor of spinning an even number? What are the odds against spinning a 2?
Experimental Probability •
Examples • 1. You roll a standard number cube. Find P (number greater than 5) • 2. A drug trial is testing the effectiveness of two drugs. If 40 patients are given Drug A, 30 patients are given Drug B, and 20 patients are given a placebo, what is the probability that a patient will not be given a placebo? • 3. What are the odds of rolling a sum of 12 using two number cubes?
More Examples • 4. In a batch of 970 calculators, 8 were found defective. What is the probability that a calculator chosen at random will be defective? Write as a percent. Round to nearest tenth of a percent if necessary. • 5. Suppose you flip a coin and roll a number cube. What is the probability of having tails come up on the coin and an even number on the number cube? • 6. Suppose you choose a marble from a bag containing 3 red marbles, 3 white marbles, and 7 blue marbles. You return the first marble to the bag and then choose again. Find P(red and blue)
More Examples • 7. In a word game, you choose a tile from a bag, replace it, and then choose another. If there are 21 vowels and 18 consonants, what is the probability you will choose a consonant and then a vowel? • 8. The names of 9 boys and 8 girls are in a hat. What is the probability of first drawing a girl’s name and then a boy’s name from the hat?
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