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2-6 Theoritical and experimental probability

2-6 Theoritical and experimental probability. Ex. 1 finding theoretical probability. Probability: how likely something will occur Outcome: result of a single trial rolling a 5 on a dice Sample space: all possible outcomes all numbers on number cube Event:

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2-6 Theoritical and experimental probability

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  1. 2-6 Theoritical and experimental probability

  2. Ex. 1 finding theoretical probability • Probability: • how likely something will occur • Outcome: • result of a single trial • rolling a 5 on a dice • Sample space: • all possible outcomes • all numbers on number cube • Event: • any outcome or group of outcomes • Theoretical probability: • number of favorable outcomes/number of possible outcomes

  3. Ex. 1 cont. • A bowl contains 12 slips of paper, each with a different name of a month. Find the theoretical probability that a slip selected at random has a name of a month that starts with J. • Simplify fractions

  4. Ex. 2 finding complement • Complement of an event: • all outcomes not in an event • To find: • P(not an event) = 1 – P(event) • On a popular television game show, a contestant must choose one of five envelopes. One contains a car. Find the probability of not finding a car • P(not car) = 1 – P(car) • P(not car) = 1 - • P(not car) =

  5. Ex. 3 Finding odds • Odds: • compares favorable and nonfavorableoutcomes • 2 ways • Odds in favor: • Number of favorable: number of unfavorable • Odds against: • Number of unfavorable: number of favorable • Find odds in favor landing on a number greater than or equal to 6 • Favorable: 6, 7, 8 • Unfavorable: 1, 2, 3, 4, 5 • Odds in favor is 3:5 • Reduce if possible

  6. Ex. 3 cont • Find the odds against landing on a number less than 3. • Odds against = unfavorable: favorable • Unfavorable – 4, 5, 6, 7, 8, 9 • Favorable – 1, 2, 3 • Odds against is 6:2 • Reduce • 3:1

  7. Ex.4 experimental probability • Experimental probability: • number of times an event occurs/number of times experiment is done • After receiving complaints, a skateboard manufacturer inspected 1000 skateboards at random. The manufacturer found no defects in 992 skateboards. What is the probability that a skateboard selected at random had no defects? Write as a percent. • P(no defect) = .992 • Move decimal 2 places to right • 99.2%

  8. Ex. 4 cont • Your practice • Pg 96 number 23 • P(trade school) = • P(trade school) = .24 • Move decimal 2 places to right • 24%

  9. Ex. 5 Using Experimental Probability • The same manufacturer has 8976 skateboards in its warehouse. If the probability that a skateboard has no defects is 99.2%, predict how many skateboards are likely to have no defect. • Number with no defects = P(no defects) X number of skateboards • s = skateboards • s = 99.2% X 8976 • Convert % to decimal • s = .992 X 8976 • s = 8904.192 • s = 8904

  10. Ex. 5 Cont • A manufacturer inspects 700 light bulbs. She finds that the probability that a light bulb works is 99.6%. There are 35,400 light bulbs in the warehouse. Predict how many light bulbs are likely to work. • Bulbs = P(works) X total bulbs • b = bulbs • b = 99.6% X 35,400 • b = .996 X 35,400 • b= 35,258.4 • b = 35,258

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