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12.3 – Conditional Probability

12.3 – Conditional Probability. Given that A and B are dependent events, the conditional probability of an event B , given that event A has already occurred, is P( B | A ) = P( A and B ) P( A ).

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12.3 – Conditional Probability

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  1. 12.3 – Conditional Probability

  2. Given that A and B are dependent events, the conditional probability of an event B, given that event A has already occurred, is P(B|A) = P(A and B) P(A)

  3. Given that A and B are dependent events, the conditional probability of an event B, given that event A has already occurred, is P(B|A) = P(A and B) P(A) Ex. 1 If a die is rolled, what is the probability that a 3 was rolled given that the number is odd

  4. Given that A and B are dependent events, the conditional probability of an event B, given that event A has already occurred, is P(B|A) = P(A and B) P(A) Ex. 1 If a die is rolled, what is the probability that a 3 was rolled given that the number is odd P(3|odd)

  5. Given that A and B are dependent events, the conditional probability of an event B, given that event A has already occurred, is P(B|A) = P(A and B) P(A) Ex. 1 If a die is rolled, what is the probability that a 3 was rolled given that the number is odd P(3|odd) = P(odd and 3)

  6. Given that A and B are dependent events, the conditional probability of an event B, given that event A has already occurred, is P(B|A) = P(A and B) P(A) Ex. 1 If a die is rolled, what is the probability that a 3 was rolled given that the number is odd P(3|odd) = P(odd and 3) P(odd)

  7. Given that A and B are dependent events, the conditional probability of an event B, given that event A has already occurred, is P(B|A) = P(A and B) P(A) Ex. 1 If a die is rolled, what is the probability that a 3 was rolled given that the number is odd P(3|odd) = P(odd and 3) P(odd)

  8. Given that A and B are dependent events, the conditional probability of an event B, given that event A has already occurred, is P(B|A) = P(A and B) P(A) Ex. 1 If a die is rolled, what is the probability that a 3 was rolled given that the number is odd P(3|odd) = P(odd and 3) P(odd) = 1/6

  9. Given that A and B are dependent events, the conditional probability of an event B, given that event A has already occurred, is P(B|A) = P(A and B) P(A) Ex. 1 If a die is rolled, what is the probability that a 3 was rolled given that the number is odd P(3|odd) = P(odd and 3) P(odd) = 1/6 1/2

  10. Given that A and B are dependent events, the conditional probability of an event B, given that event A has already occurred, is P(B|A) = P(A and B) P(A) Ex. 1 If a die is rolled, what is the probability that a 3 was rolled given that the number is odd P(3|odd) = P(odd and 3) P(odd) = 1/6 = 1/3 1/2

  11. Ex. 2 Find the probability that a test subject stayed healthy, given that he or she used an experimental drug.

  12. Ex. 2 Find the probability that a test subject stayed healthy, given that he or she used an experimental drug. Total = 4000

  13. Ex. 2 Find the probability that a test subject stayed healthy, given that he or she used an experimental drug. Total = 4000 P(H|D)

  14. Ex. 2 Find the probability that a test subject stayed healthy, given that he or she used an experimental drug. Total = 4000 P(H|D) = P(H and D)

  15. Ex. 2 Find the probability that a test subject stayed healthy, given that he or she used an experimental drug. Total = 4000 P(H|D) = P(H and D) P(D)

  16. Ex. 2 Find the probability that a test subject stayed healthy, given that he or she used an experimental drug. Total = 4000 P(H|D) = P(H and D) P(D) = 800/4000

  17. Ex. 2 Find the probability that a test subject stayed healthy, given that he or she used an experimental drug. Total = 4000 P(H|D) = P(H and D) P(D) = 800/4000 2400/4000

  18. Ex. 2 Find the probability that a test subject stayed healthy, given that he or she used an experimental drug. Total = 4000 P(H|D) = P(H and D) P(D) = 800/4000 = 800/2400 2400/4000

  19. Ex. 2 Find the probability that a test subject stayed healthy, given that he or she used an experimental drug. Total = 4000 P(H|D) = P(H and D) P(D) = 800/4000= 800/2400= 1/3 2400/4000

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