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Agenda – Thurs. June 7 ( Day 2)

Agenda – Thurs. June 7 ( Day 2). Recap: Probability Versus Odds Probabilities Using Counting Techniques (6.3) Homework Today I will… “Apply the counting techniques from Chapters 4 and 5 to probability problems.”. 6.3 Probabilities Using Counting Techniques.

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Agenda – Thurs. June 7 ( Day 2)

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  1. Agenda – Thurs. June 7 (Day 2) • Recap: Probability Versus Odds • Probabilities Using Counting Techniques (6.3) • Homework • Today I will… “Apply the counting techniques from Chapters 4 and 5 to probability problems.”

  2. 6.3 Probabilities Using Counting Techniques

  3. Counting Techniques Make Calculating Probability Easier! • Probability techniques can be applied to many different areas of everyday life to help predict the outcome of a particular situation. • Although card games are played by most for pure entertainment purposes and for the enjoyment of the unpredictability, it can also be interesting to apply our counting techniques to such problems. • In some situations, the possible outcomes are not easy or convenient to count individually. In many cases, the counting techniques of permutations and combinations can be helpful for calculating theoretical probabilities, or a simulation can be used to calculate an experimental probability.

  4. Example #1 • Two brothers enter a race with five friends. The racers draw numbers to determine their starting positions. What is the probability that the older brother will start in lane 1 with his brother beside him in lane 2? Let B = older bro in lane 1 and younger in lane 2 5! 1 = = n(B) 7! 42 P(B) = n(S)

  5. Example #2 • A focus group of three members is to be randomly selected from a medical team consisting of five doctors and seven technicians. a) What is the probability that the focus group will be comprised of doctors only? Let D = doctors only 10 1 = = 5C3 n(D) 220 22 P(D) = P(D) = 12C3 n(S)

  6. Example #2 • A focus group of three members is to be randomly selected from a medical team consisting of five doctors and seven technicians. b) What is the probability that the focus group will not be comprised of doctors only? P(D’) = total - junk Indirect Method (using part a) = 1 - 1 21 = 22 22

  7. Example #3 • What is the probability that two or more people out of a group of six will have the same birthday? Assume that no one in the group was born on February 29th (leap year). Therefore, there is a 4% chance of two or more people out of group of six sharing a birthday. = 1 – 0.9595 = 0.04

  8. Example #4 • You are dealt 5 cards from a standard deck. a) Determine the probability of receiving two hearts, one diamond, one club & one spade. Let B = getting 2 hearts, one diamond, one club and one spade (13C1) (13C2) (13C1) 2197 = 6.6% = (13C1) n(B) 33320 P(B) = P(B) = 52C5 n(S)

  9. Example #4 • You are dealt 5 cards from a standard deck. b) Determine the odds in favour of receiving the hand from part a) Let B = getting 2 hearts, one diamond, one club and one spade = 2197 31123 2197 2197 31123 P(B) P(B’) = = = 1 - P(B) 33320 33320 33320 33320 33320 Odds in favour of B= P(B’) Therefore, the odds in favour are 2197: 31123

  10. Homework Page 324-325 #1, 3, 5, 8, 9, 11 Also: Review Sections 6.4 and 6.5 on your own: You will need to understand the difference between Independent and Dependent Events for your Probability Summative.

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