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Warm-up

Warm-up. Would it be fair to give a report card grade based on 1 test? or 1 assignment? Would it be accurate to conclude that a coin will always come up heads after flipping it once?

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Warm-up

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  1. Warm-up • Would it be fair to give a report card grade based on 1 test? or 1 assignment? • Would it be accurate to conclude that a coin will always come up heads after flipping it once? • If 50% of students in a class said they like country music, do you think that means 50% of students in the whole school like country music? • Could you assume that if a person throws a basketball once and makes a basket from half court, then they are a good shooter?

  2. Classical and Empirical Probability

  3. Classical/Theoretical Probability • Assumes that we are given a situation in which all outcomes are equally likely to occur.

  4. A penny and a quarter are tossed once. If this experiment is repeated 1000 times, what is the expected number of times that the results show tails for both coins? • If A is the event of getting both tails, we can write A = {(T, T)} • We can also write P(A)=

  5. Suppose that B is the event of getting one tail and one head. • Then B = {(H, T), (T, H)} and P(B) =

  6. A nickel, a quarter, and a silver dollar are tossed once. If C represents the event of getting exactly one tail and two heads, write C as a set of elements. • C = {(T, H, H), (H, T, H), (H, H, T)}.

  7. Suppose the experiment from the previous slide is repeated 736 times. What is the expected number of times that the results show exactly one tail and two heads? • P(C) = , then we can expect to get exactly one tail and two heads is

  8. An ordinary die is rolled once. Event D is defined as the set of outcomes in which a prime number is shown. What is the value of P(D)? Suppose this experiment is repeated 246 times. • D= {2, 3, 5} • P(D) =

  9. In drawing two cards from a deck of cards, one card at a time, with the replacement of the first card prior to drawing the second card. Let F represent the event of drawing 2 red jacks. What is the value of P(F)? • F = {(JD, JD), (JD, JH), (JH, JH), (JH, JD)} • So P(F) = Suppose this experiment is repeated 5408 times.

  10. Empirical/Experimental Probability • Assumes that the outcomes are not equally likely; rather, their associated probabilities are calculated based on observations or historical data.

  11. A particular die is “weighted”, which means that it tends to land on 4, 5, or 6 more often than it does on 1, 2, or 3. In rolling this die 1800 times, the results of the frequency of each outcome are as follows: Based on this chart, what is the probability that in rolling this die, it will land on a 3 or a 4?

  12. This “weighted” dime is tossed 3 times, and the experiment is repeated 4000 times. Here are the results: Based on this chart, what is the probability that when this dime is tossed three time, the result will be exactly two tails?

  13. Math Flash!!! • When computing a probability value involving coins or dice, use the classical probability approach, unless you are given a chart of observed frequencies from which the probability is to be calculated.

  14. Theoretical or Experimental • Maria flipped a coin and got 6 heads out of 10 flips. • Carlos said the chances of rain today are 30%. • James said he has a 70% chance of making a free throw because yesterday he made 7 out of 10. • 6 students out of 18 students in one classroom caught a cold, so the nurse said about 33% of the students in school would catch the same cold. • Julia placed an eraser under one of four cups and told Patrick he had a 25% chance of finding the correct cup.

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