5.4 Conditional Probability Chapter 5 Probability 5.4 Conditional Probability

EXAMPLE Computing Conditional Probabilities The following data represent the language spoken at home by age for residents of San Francisco County, CA between the ages of 5 and 64 years. Source: United States Census Bureau, 2000 Supplementary Survey

(a) Compute the probability that a randomly selected resident who speaks Spanish at home is 5 - 17 years old. (b) Compute the probability that a randomly selected resident who is 5 - 17 years old speaks Spanish at home.

EXAMPLE Murder Victims In 1998, 17.8% of all murder victims were between the ages of 20 and 24 years old. Also in 1998, 15.3% of all murder victims were male and between 20 and 24 years old. What is the probability that a randomly selected murder victim in 1998 was male given that the victim is 20 - 24 years old?

EXAMPLE Checking for Independence The following data represent the language spoken at home by age for residents of San Francisco County, CA between the ages of 5 and 64 years. Determine whether the events “Spanish” and “5-17 years” are independent.

Caution! Mutually exclusive and independent are not synonymous.