Learning Target: I Can Find the Probabilities of Events

9.7 – Probability

Learning Target: I can find the probabilities of events

Probability – if an event can ______in s ways and ______in f ways, then its probability is .

EX: A bag contains 3 red balls and 5 green balls. If one ball is selected at random what is the probability that it is red?

What is the probability that it is green?

Notice that probabilities must always add to __:

EX: One bag of gummy worms contains 15 red, 10 yellow, and 6 green. Find the probability of each selection.

a.) One red

b.) Not picking a yellow

c.) Picking one green

d.) Not picking a red

Odds – the ____ of successful ______to failures

EX: What are the odds of drawing a 5 from a standard deck of 52 cards? EX: On an ACT Review Guide, there are 5 math questions and 4 science questions. Arthur picks a question at random to answer. What are the odds of not picking a science question?

EX: What are the odds that a person chosen at random got a passing grade on an algebra test if the scores were 3 A’s, 4 B’s, 10 C’s, 2 D’s, and 2 F’s?

Probability of Two Independent Events:

If two events A and B are ______, then the probability of both events occurring is found by P(A and B)=______

EX: A bag contains 5 red marbles and 4 white marbles. A marble is to be selected and replaced in the bag. A 2nd selection is then made. What is the probability of selecting 2 red marbles?

EX: A box contains 5 triangles, 6 circles, and 4 squares. If a figure is removed, replaced, and a second is picked, what is the probability that a triangle and then a circle will be picked? EX: A jar contains 7 lemon gumdrops, 3 cherry gumdrops, and 8 rainbow gumdrops. What is the probability of selecting 2 lemon in succession providing each gumdrop is replaced?

Probability of Two Dependent Events:

If 2 events A and B are dependent, then the probability of both events occurring is found by P(A and B)=______

EX: There are 7 dimes and 9 pennies in a purse. Suppose two coins are to be selected at random, without replacing the first one. Find the probability of picking a penny and then a dime.

EX: What is the probability of drawing 2 cards showing odd numbers from a set of cards that show the first 20 counting numbers if the 1st card is not replaced?

EX: There are 3 quarters, 4 dimes, and 7 nickels in a change purse. Suppose 3 coins are to be selected without replacement. What is the probability of selecting a quarter, then a dime, and then a nickel?

Mutually Exclusive – events that ______occur at the _____ time

______Events – two events that can occur at the same time EX: What is the probability of drawing a jack or a king from a standard deck of cards?

EX: A card is selected from a standard deck of cards. What is the probability that it is a red card or an ace?

EX: 3 cards are selected from a standard deck. What is the probability of selecting a king, queen, or a red card?

EX: An Easter basket contains 45 dyed eggs: 15 yellow, 12 green, and 18 red. What is the probability of selecting a green or red egg?

EX: The letters from the word LOVE and LIVE are placed on cards and but in a box. What is the probability of selecting an L or O from the box? EX: The letters of the alphabet are placed in a bag. What is the probability of selecting a vowel or the letters QUIZ?

EX: Two coins are tossed. What is the probability that one will land heads up and the other will land hands down?

EX: A card is drawn from a standard deck of playing cards. What is the probability that the card is a heart?

EX: A 6-sided die is tossed twice. What is the probability that the total of the 2 tosses is 5?

EX: A card is selected from a standard deck. What is the probability that the card is either a club or an ace?

EX: Two integers from 1 to 30 are chosen by a random number generator. What is the probability that both numbers are less than 12? EX: A sales representative makes a sale at approximately one-third of all calls. If, on a given day, the representative contacts five potential clients, what is the probability that a sale will be made with each of the five contacts?

EX: A sales rep makes a sale at approximately one-third of all calls. If, on a given day, the representative contacts 5 potential clients, what is the probability that a sale will be made with AT LEAST one contact?

HW Pg.709 3-48 3rds

Quiz 9.5-9.7 tomorrow (Wednesday due to ACT Testing)