Math Studies conditional probability

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Math Studies conditional probability

  1. 1. Conditional Probability Math Studies Diploma Programme
  2. 2. Conditional Probability Conditional Probability contains a condition that may limit the sample space for an event. You can write a conditional probability using the notation P ( B A)- This reads “the probability of event B, given event A”
  3. 3. Conditional Probability The table shows the results of a class survey. Find P(own a pet | female) Do you own a pet? yes no female 8 6 14 females; male 5 7 13 males The condition female limits the sample space to 14 possible outcomes. Of the 14 females, 8 own a pet. Therefore, P(own a pet | female) equals 8 . 14
  4. 4. Conditional Probability The table shows the results of a class survey. Find P(wash the dishes | male) Did you wash the dishes last night? yes no female 7 6 13 females; male 7 8 15 males The condition male limits the sample space to 15 possible outcomes. Of the 15 males, 7 did the dishes. Therefore, P(wash the dishes | male) 7 15
  5. 5. Let’s Try OneUsing the data in the table, find the probability that a sample of notrecycled waste was plastic. P(plastic | non-recycled) The given condition limits the Material Recycled Not Recycled sample space to non-recycled Paper 34.9 48.9 waste. Metal 6.5 10.1 Glass 2.9 9.1 A favorable outcome is Plastic 1.1 20.4 non-recycled plastic. Other 15.3 67.8 20.4 P(plastic | non-recycled) = 48.9 + 10.1 + 9.1 + 20.4 + 67.8 20.4 = 156.3 0.13 The probability that the non-recycled waste was plastic is about 13%.
  6. 6. Conditional Probability Formula The conditional probability that A occurs given that B has occurred is written as P(A B) and is defined as: P(A ∩ B) P(A B) = P(B)
  7. 7. Problem Solving with Venn DiagramIn a class of 29 students, 20 students study French, 15students study Malay, and 8 students study bothlanguages. A student is chosen at random from the class.Find the probability that the students:a.Studies Frenchb.Studies neither languagec.Studies at least one languaged.Studies both languagese.Studies Malay given that they study Frenchf.Studies French given that they study Malayg.Studies both language given that they study at least oneof the languages
  8. 8. Venn Diagram F M 12 7 8 2
  9. 9. Find the probability that a person chosen at random:a.is in Ab.is not in either A or Bc.is not in A and not in Bd.is in A, given that they are not in Be.is in B, given that they are in Af.is in both A and B, given that they are in A A B 15 8 12 5
  10. 10. Find the probability that a person chosen at random:a.is in Ab.is not in either A or Bc.is not in A and not in Bd.is in A, given that they are not in Be.is in B, given that they are in Af.is in both A and B, given that they are in A A B 15 8 12 5

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