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In Section #1: EX1

In Section #1: EX1. Possible outcomes at 1 st stoplight: { } Possible outcomes at 2 nd stoplight: { } Possible outcomes at 3 rd stoplight: { } Sample Space: S = {. Red, Green, Yellow. Red, Green, Yellow. Red, Green, Yellow.

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In Section #1: EX1

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  1. In Section #1: EX1 Possible outcomes at 1st stoplight: { } Possible outcomes at 2nd stoplight: { } Possible outcomes at 3rd stoplight: { } Sample Space: S = { Red, Green, Yellow Red, Green, Yellow Red, Green, Yellow RRR, GRR, YRR, RGR, GGR, YGR, RYR, GYR, YYR, RRG, GRG, YRG,RGG, GGG, YGG, RYG, GYG, YYG, RRY, GRY, YRY, RGY, GGY, YGY, RYY, GYY, YYY}

  2. In Section #1: EX1 3 # of possible outcomes at 1st stoplight: ________ # of possible outcomes at 2nd stoplight: _______ # of possible outcomes at 3rd stoplight: ________ Total number of outcomes in the sample space: _______ 3 3 27

  3. In Section #1: EX2 Possible outcomes when picking a number: { } Possible outcomes when flipping a coin: { } Sample Space: S = { 1, 2, 3, 4, 5 Heads, Tails 1T, 1H, 2T, 2H, 3T, 3H, 4T, 4H, 5T, 5H, 6T, 6H}

  4. In Section #1: EX1 5 # of possible outcomes when picking a number: ________ # of possible outcomes flipping a coin: _______ Total number of outcomes in the sample space: _______ 2 10

  5. In Section #1: EX1 How can you use the number of outcomes of each event (or level in the tree diagram to find the total number of possible outcomes in a sample space? Multiply the number of outcomes For each event together

  6. Finding Total Number of Outcomes Multiply the number of possible outcomes at each “level” of the tree diagram.

  7. Finding Total Number of Outcomes Example: Lindsay is getting ready for school. She has three shirts, 4 pairs of pants and 3 pairs of shoes to choose from. How many possible outcomes could she have for an outfit of one shirt, one pair of pants and one pair of shoes?

  8. Finding Total Number of Outcomes Example: Number of shirts = 3 Number of pants = 4 Number of shoes = 3 Total number of outcomes: 3 * 4 * 3 = 36

  9. Section 2 EX1: EX: Using a deck of cards, find P(4 or 6) List all of the 4’s: { }List all of the 6’s: { } How many 4’s are in the deck?____How many 6’s are in the deck?____ How many cards are both a 4 and a 6 at the same time?_____ (Circle them) 4 4 0

  10. Section 2 EX2: EX: Using a deck of cards, find P(Ace or clubs) List all of the Ace’s: { }List all of the Clubs: { } How many Ace’s are in the deck?____How many clubs are in the deck?____ How many cards are both an Ace and a Club at the same time?_____ (Circle them) 4 13 1

  11. Section 2 EX3: EX: Rolling a die, find P(greater than 2 or even) List all of the numbers greater than 2: { }List all of the even numbers: { } How many #s are greater than 2?____How many #s are even?____ How many numbers are both greater Than 2 or even?____ (Circle them) 3, 4, 5, 6 2, 4, 6 4 3 2

  12. Section 2 EX4: EX: Rolling a die, find P(less than 3 or greater than 4) List all of the numbers less than 3: { }List all of the numbers greater than 4: { } How many #s are less than 3?____How many #s are greater than 4?____ How many #s are both less than 3 Or greater than 4?____ (Circle them) 1, 2 5, 6 2 2 0

  13. Finding Total Number of Outcomes Multiply the number of possible outcomes at each “level” of the tree diagram.

  14. Finding Total Number of Outcomes Example: Lindsay is getting ready for school. She has three shirts, 4 pairs of pants and 3 pairs of shoes to choose from. How many possible outcomes could she have for an outfit of one shirt, one pair of pants and one pair of shoes?

  15. Finding Total Number of Outcomes Example: Number of shirts = 3 Number of pants = 4 Number of shoes = 3 Total number of outcomes: 3 * 4 * 3 = 36

  16. Mutually Exclusive Two events are mutually exclusive if they cannot occur at the same time *They have no outcomes in common

  17. Are they Mutually Exclusive? Which of the following are mutually exclusive? • Getting a 7 and getting a jack • Getting a club and getting a king • Getting a face card and getting an ace • Getting a face card and getting a spade A and C are mutually exclusive

  18. P(A or B) for Mutually Exclusive When two events A and B are mutually exclusive, the probability that A or B will occur is: P(A or B) = P(A) + P(B)

  19. Mutually Exclusive Venn Diagram P(jack or a 7) Jack 7

  20. Given a deck of cards, find P(jack or a 7): P(jack or a 7) = P(jack) + P(7) = 4/52 + 4/52 = 8/52 = 2/13

  21. P(A or B) for NOT Mutually Exclusive If A and B are NOT mutually exclusive (they have an outcome in common) then the probability that A or B will occur is: P(A or B) = P(A) + P(B) – P(A and B)

  22. NOT Mutually Exclusive Venn Diagram P(heart or ace) Heart Ace

  23. Given a deck of cards, find P(heart or ace): P(heart or ace) = P(heart) + P(ace) – P(heart and ace) = 13/52 + 4/52 – 1/52 = 16/52 = 4/13

  24. Practice Problems 1. A box contains 20 red, 10 blue and 30 yellow beads. What is the probability of a bead drawn at random being: a) red or blue? b) yellow or blue? c) red, blue or yellow?

  25. Practice Problems 2. The letters of the words ‘HELLO’ and ‘THERE’ are written on individual cards and the cards placed into a bag. A card is picked at random. What is the probability of picking: a) the letter ‘L’ b) the letter ‘E’c) the letter ‘L’ or ‘E’d) a consonante) the letter ‘E’ or a consonantf) the letter ‘L’, ‘E’ or ‘T’

  26. Practice Problems 3. A set of cards with a letter on each card as shown below are placed into a bag. Howard picks a card at random from the bag. U E A R Q H C H L A Determine the probability that the card is:a) an E. b) not an E. c) not a vowel. d) a P. e) not a P. f) either a Q or U or Hg) not a Q, U or H.

  27. Practice Problems 4. A number is chosen at random from a set of whole numbers from 1 to 50. Calculate the probability that the chosen number: a) is not less than 45b) is not a multiple of 4c) is more than 45d) is not more than 45

  28. Practice Problems 5. You have a bag with 10 clear marbles numbered 1-10, 10 brown marbles numbered 1-10 and 10 pink marbles numbered 1-10. Find the probability that the chosen number: a) is a 7 or a clear marble b) is an even number or a pink marble c) is a brown marble or a number greater than 8 d) is a number greater than 10 or a pink marble e) a pink marble or a clear marble f) a number greater than 7 or a number less than 3

  29. Practice Problems 1. A box contains 20 red, 10 blue and 30 yellow beads. What is the probability of a bead drawn at random being: a) red or blue? b) yellow or blue? c) red, blue or yellow? 30/60 = 1/2 40/60 = 2/3 60/60 = 1

  30. Practice Problems 2. The letters of the words ‘HELLO’ and ‘THERE’ are written on individual cards and the cards placed into a bag. A card is picked at random. What is the probability of picking: a) the letter ‘L’ b) the letter ‘E’c) the letter ‘L’ or ‘E’d) a consonante) the letter ‘E’ or a consonantf) the letter ‘L’, ‘E’ or ‘T’ 2/10 = 1/5 3/10 5/10 = 1/2 6/10 = 3/5 9/10 6/10 = 3/5

  31. Practice Problems 3. A set of cards with a letter on each card as shown below are placed into a bag. Howard picks a card at random from the bag. U E A R Q H C H L A Determine the probability that the card is:a) an E. b) not an E. c) not a vowel. d) a P. e) not a P. f) either a Q or U or Hg) not a Q, U or H. 1/10 9/10 6/10 = 3/5 0 1 4/10 = 2/5 6/10 = 3/5

  32. Practice Problems 4. A number is chosen at random from a set of whole numbers from 1 to 50. Calculate the probability that the chosen number: a) is not less than 45b) is not a multiple of 4c) is more than 45d) is not more than 45 6/50 = 3/25 38/50 = 19/25 5/50 = 1/10 45/50 = 9/10

  33. Practice Problems 5. You have a bag with 10 clear marbles numbered 1-10, 10 brown marbles numbered 1-10 and 10 pink marbles numbered 1-10. Find the probability that the chosen number: a) is a 7 or a clear marble b) is an even number or a pink marble c) is a brown marble or a number greater than 8 d) is a number greater than 10 or a pink marble e) a pink marble or a clear marble f) a number greater than 7 or a number less than 3 12/30 = 2/5 14/30 = 7/15 20/30 = 2/3 20/30 = 2/3 10/30 = 1/3 15/30 = 1/2

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