Basic Rules of Probability Vocabulary experiment sample space

Basic Rules of Probability

Vocabulary • experiment • sample space - the set S of all possible outcomes of an experiment • event – any subset E of the sample space S • probability – success divided by total • odds – success to failures

Vocabulary • mutually exclusive - events that cannot occur at the same time

Determine if the following events mutually exclusive. • E is the event of “being a doctor” and F is the event of “being a women” • E is the event of “being single” and F is the event of “being married” • E is the event of “being a plumber” and F is the event of “being a stamp collector”

Formulas

Probability Rules

Probability Rules if E and F are mutually exclusive

Find the probability of each of the following: • a jack and a heart • a jack or a heart • not a jack of hearts • above a jack • below a three

Find the probability of each of the following: • both above a jack and below a three • either above a jack or below a three • not a jack of hearts • above a five • below a jack

If o(E) = 1: 6, then find .

Rolling a Pair of Dice

Find the probability that the sum when a pair of dice is rolled is • 8 or 10 • even and less than 5 • even or less than 5

Alex is taking two courses, algebra and U. S. history. Student records indicate that the probability of passing algebra is. 35, that of failing U. S. history is. 45, and that of passing at least one of the two courses is. 80. Find the probability that • Alex will pass history • Alex will pass both courses

Alex is taking two courses, algebra and U. S. history. Student records indicate that the probability of passing algebra is. 35, that of failing U. S. history is. 35, and that of passing at least one of the two courses is. 80. Find the probability that • Alex will fail both courses • Alex will pass exactly one course

Formulas (conditional probability)

In a newspaper poll concerning violence on television, 600 people were asked, "What is your opinion of the amount of violence on prime-time television -- is there too much violence on television? ". Their responses are summarized in the table below. Yes No Don’t Know Men 162 95 23 280 Women 256 45 19 320 Total 418 140 42 600 Total

Yes No Don’t Know Men 162 95 23 280 Women 256 45 19 320 Total 418 140 42 600 • p(yes) • p(men) • p(yes | men) • p(men | yes) • p(yes men) • p(men yes) Total

Cards are dealt from a full deck of 52. Find the probability of each of the given events. • the first card is a diamond • the second card is a spade, given that the first card was a diamond • the first card is a diamond and the second card is a spade • draw a tree diagram illustrating this

A personal computer manufacturer buys 38% of its chips from Japan and the rest from America. 1. 7% of the Japanese chips are defective, and 1. 1% of the American chips are defective. • Find the probability that a chip is defective and made in Japan. • Find the probability that a chip is defective and made in America. • Find the probability that a chip is defective. • Find the probability that a chip is defect-free.