9 5 Conditional Probability Independent Events Conditional probability is probability based on additional information that reduces the sample space that is the probability of event A given that event B has already occurred P E F written P A B Thus P E F P F P F 0 Product Rule P E F P F P E F or P E F P E P F E E and F are independent events if P F E P F or P E F P E Product Rule for Independent Events E and F are independent events if and only if P E F P F P E Enrollment Status of U S Population 3 Years Old and Over by Sex October 2004 Numbers in thousands civilian non institutionalized population Both Sexes Male M Female F Population Number Enrolled in School S Elementar y E 32 556 High School H 16 791 College C 75 461 Nursery or Kindergarten K 8 731 277 467 135 510 141 957 37 449 38 012 4 642 4 089 16 834 15 722 8 398 8 393 7 575 9 808 Find the probability of 1 That a person is in elementary school the given that the person is male school 3 That a person is in college given that that the person is enrolled in school 5 17 383 2 That a person is male given that person is in elementary 4 That a person is in college given the person is female The table below gives the distribution of registered voters in one state based on the voter s sex Femal e Male Democra t 22 Republic an 7 Independent 20 28 9 14 What is the probability that a randomly selected registered voter was a a female given that the person was b a Democrat given that person was a a Republican male c female and independent d male 6 A certain car has a three year warranty Four percent of these cars break down within three years If two cars are chosen at random what is the probability that both will break down before the expiration of the warranty 7 In the game of Yatzee five die are rolled What is the probability of a 2 appearing on all five die 8 Given P E 48 P F 53 and P E F 75 find P F E 9 Draw a tree diagram to find the probability of drawing three fives out of a standard 52 card deck if three cards are drawn without replacement What is the probability of drawing two fives in three draws