5 3 Conditional Probability and Independence Conditional Probability

5. 3: Conditional Probability and Independence

Conditional Probability

EX 12: The following table gives the favorite subject by gender: a. What is the probability that a randomly selected b. student is male? Subject Math Science English Other Total Male 15, 802 3, 262 3, 822 1, 571 24, 457 Female 2, 367 2, 233 856 571 6, 027 b. What is the probability that a student likes math, given that it was a male? a female? c. What is the probability that a student is female, given that she likes science? Totals 18, 169 5, 495 4, 678 2, 142 30, 484

The General Multiplication Rule The probability that events A and B both occur can be found using the general multiplication rule P(A ∩ B) = P(A) • P(B | A) Conditional Probability and Independence Two events A and B are independent if P(A | B) = P(A) and P(B | A) = P(B).

EX 13: No replacement A poker player wants to draw two diamonds in a row, and there already 11 cards on the table, 4 of which are diamonds. What is the probability that both cards will be diamonds? Only 41 cards left in the deck Only 9 diamonds left in the deck

EX 14: A study found that 66% of Basha students have parasitic worms. There is a test for worms. When students really do have worms, the test shows positive 98. 9% of the time. When they don’t have worms, the test shows negative 99% of the time. Draw a tree diagram. . 66. 34 . 989 + . 011 - worm No worm . 01 + . 99 What is the probability that someone will test positive for worms? What is the probability that someone has worms, provided they tested positive?