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Chapter 6 Review

Chapter 6 Review. By: Manpretty , Zunaira , Gaganvir and Armani. 6.1- Basic Probability Concepts. An event is a collection of outcomes satisfying a particular condition. The probability of an event can range between 0 (impossible) and 1 or 100% (certain)

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Chapter 6 Review

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  1. Chapter 6Review By: Manpretty, Zunaira, Gaganvir and Armani

  2. 6.1- Basic Probability Concepts • An event is a collection of outcomes satisfying a particular condition. The probability of an event can range between 0 (impossible) and 1 or 100% (certain) • The empirical probability of an event is the number of times the event occurs divided by the total number of trials • The theoretical probability of an event A is given by P(A)=n(A)/n(S), where n(A) is the # of outcomes making up A, n(S) is the total # of outcomes • Subjective probability is based on previous experience or guesswork • If the probability of event A is given by P(A), then the probability of the complement of A is given by P(A’)=1-P(A)

  3. 6.2- Odds • Odds in favor of A are given by the ratio P(A)/P(A’) • Odds against A are given by the ratio P(A’)/P(A) • If odds are in favor of A are h/k, then P(A)=h/h+k • Ex: If the chance of a snowstorm in January is estimated at 0.4, what are the odds against having a snowstorm next January? Is a January storm more likely than not? Let event A=(snowstorm) Since P(A)+ P(A’)=1,odds against A= P(A’)/P(A) = 1-P(A)/P(A) = 1-0.4/0.4 = 0.6/0.4 = 3/2 Odds against are 3:2, which is greater than 1:1 therefore a storm is less likely to occur than not.

  4. 6.3-Probabilities using counting techniques • Permutations are useful when order is important in the outcomes; combinations are useful when order in not important • Ex: The expert group of 4 members selects students from lower grades to write a diagnostic test. Five students are from grade 10 and seven students are from grade 11. What is the probability that the expert group will be comprised of grade 10 students only? n(A)=5C4 n(S)=12C4 = 5 = 495 P(A)=n(A)/n(S) = 5/495 = 0.010

  5. 6.4- dependent and independent variables • Compound Events involve two or more separate events • Independent Events the occurrence of one event has no effect on the outcome of another • Dependents Events the occurrence of one event directly depends on the outcome of the other event • The product Rule for Independent EventsLet A & B be independent events. Then:P(AnB)=P(A)-P(B) • The product rule for dependent events P(B\A)= P(AnB)/P(A)

  6. Continued… Example: What is the probability of rolling a 3 with a dice, and drawing a 3 with a deck of cards? Answer: P(A n B) = 1/6 x 4/52 = 1/78

  7. 6.5-Mutually Exclusive Events • If two event sets have no objects in common, they are said to be mutually exclusive events • Mutually exclusive: P(A or B)= P(A) + P(B) • Non- mutually exclusive: P(A or B)= P(A) + P(B)- P(A and B) • Example: If a voltage spike has a 0.2% probability of damaging the product’s power supply, a 0.6% probability of damaging downstream components, and a 0.1% probability of damaging the power supply and other components. Determine the probability that a voltage spike will damage the product. Answer: P(A or C)= P(A) + P(C) – P(A and C) = 0.2% + 0.6%- 0.1% = 0.7%

  8. To prepare for the test do the chapter test questions! GOODLUCK 

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