Algebra IIAlgebra II

10.4: Find Probabilities of Disjoint 10.4: Find Probabilities of Disjoint and Overlapping Eventsand Overlapping Events

HW: HW: p.710 (8 – 38 even)

Chapter 10 Test: Thursday

Overlapping EventsOverlapping EventsTwo events are overlapping if they have one Two events are overlapping if they have one

or more or more outcomes in commonoutcomes in common..

P(A or B) = P(A) + P(B) – P(A and B)P(A or B) = P(A) + P(B) – P(A and B)

Disjoint EventsDisjoint EventsTwo events are disjoint, or mutually exclusive, Two events are disjoint, or mutually exclusive,

if they have if they have no outcomes in common. no outcomes in common.

P(A or B) = P(A) + P(B)P(A or B) = P(A) + P(B)

A B

Events A and B are disjoint. Events A and B are disjoint. Find P(A or B).Find P(A or B).

1.) P(A) = 0.2, P(B) = 0.31.) P(A) = 0.2, P(B) = 0.3

2.) P(A) = 34%, P(B) = 45%2.) P(A) = 34%, P(B) = 45%

Find the indicated probability.Find the indicated probability.1.) P(A) = 47%, P(B) = 21%, 1.) P(A) = 47%, P(B) = 21%,

P(A or B) = 0.25, P(A and B) = ____________.P(A or B) = 0.25, P(A and B) = ____________.

2.) P(A) = 0.25, P(B) = 0.32, 2.) P(A) = 0.25, P(B) = 0.32,

P(A or B) = 0.45, P(A and B) = ____________.P(A or B) = 0.45, P(A and B) = ____________.

A cardA card is randomly drawn from a standard is randomly drawn from a standard deck of 52 cards. Find the probability of deck of 52 cards. Find the probability of

drawing the indicated card. drawing the indicated card.

1.) A heart or a diamond1.) A heart or a diamond

2.) A spade or an even card2.) A spade or an even card

A cardA card is randomly drawn from a standard is randomly drawn from a standard deck of 52 cards. Find the probability of deck of 52 cards. Find the probability of

drawing the indicated card. drawing the indicated card.

3.) A 6 or a 73.) A 6 or a 7

4.) An ace or a spade4.) An ace or a spade

A cardA card is randomly drawn from a standard is randomly drawn from a standard deck of 52 cards. Find the probability of deck of 52 cards. Find the probability of

drawing the indicated card. drawing the indicated card.

5.) An ace and a spade5.) An ace and a spade

6.) A face card and a 46.) A face card and a 4

7.) A spade and an even card7.) A spade and an even card

Algebra IIAlgebra II

10.5: Find Probabilities of 10.5: Find Probabilities of Independent and Dependent Independent and Dependent

EventsEvents

HW: worksheetHW: worksheet

A jar contains 10 blue, 4 red,&6 white marbles. A jar contains 10 blue, 4 red,&6 white marbles.

1.) Find the probability of choosing a red, 1.) Find the probability of choosing a red, then a white marble with replacement.then a white marble with replacement.

2.) Find the probability of choosing a red, 2.) Find the probability of choosing a red, then a white marble without replacement.then a white marble without replacement.

A jar contains 10 blue, 4 red,&6 white marbles.A jar contains 10 blue, 4 red,&6 white marbles.

3.) Three marbles are chosen with 3.) Three marbles are chosen with replacement, find the probability that they replacement, find the probability that they are not white.are not white.

A jar contains 10 blue, 4 red,&6 white marbles.A jar contains 10 blue, 4 red,&6 white marbles.

4.) Three marbles are chosen without 4.) Three marbles are chosen without replacement, find the probability where at replacement, find the probability where at least one marble is white.least one marble is white.

Find the probability of drawing the given Find the probability of drawing the given cards from a standard deck of 52 cards cards from a standard deck of 52 cards

(a) with replacement and (a) with replacement and (b) without replacement. (b) without replacement.

1.) a heart, then a spade1.) a heart, then a spade

Find the probability of drawing the given Find the probability of drawing the given cards from a standard deck of 52 cards cards from a standard deck of 52 cards

(a) with replacement and (a) with replacement and (b) without replacement. (b) without replacement.

2.) a king, then a queen2.) a king, then a queen

Find the probability of drawing the given Find the probability of drawing the given cards from a standard deck of 52 cards cards from a standard deck of 52 cards

(a) with replacement and (a) with replacement and (b) without replacement. (b) without replacement.

3.) a 10, then a 10, then another 103.) a 10, then a 10, then another 10

Find the probability of drawing the given Find the probability of drawing the given cards from a standard deck of 52 cards cards from a standard deck of 52 cards

(a) with replacement and (a) with replacement and (b) without replacement. (b) without replacement.

4.) a 4, then a 3, then a 24.) a 4, then a 3, then a 2