Suppose you were given the following box of Christmas ornaments that contains 14 silver ornaments, 12 red ornament, and 8 green ornaments. What is the probability of randomly choosing a red or green ornament from the box?

Step 1:List the events:

EventA _________

Event B __________

Decide if the events are mutually exclusive or not.

The events ______mutually exclusive because one solid colored ornament ______be red and green at the same time.

The events are mutually exclusive, so we should use the equation _____________because P(A and B) = 0.

How many total ornaments are in the box?

14 silver ornaments + _______ red ornaments + 8 green ornaments = __________ ornaments.

P(RorG)=P(R)+P(G)

P(RorG)=1=12/34+________

P(RorG)=20/34

P(RorG)=________

This means that ______ out of every 17 ornaments in the box is a red or green ornament.

A local high school has 1400 students; 800 of whom are girls. 300 of the students are seniors; of which 200 are girls. If we chose a student at random, what is the probability that we would choose a girl or a senior?

Event A: __________

Event B: __________

The events _______ mutually exclusive because one student _________ be a girl and a senior at the same time.

The events are not mutually exclusive so we should use the equation ____________________________ because P(A and B) 0

How many total students attend the school? ____________ students

P(GorS)=P(G)+P(S)P(GandS)

P(GorS)=800/1400+__________-200/1400

P(GorS)=__________

P(GorS)=9/14

The probability of choosing a student who is a girl or a senior is 9/14. This means that 9 out every _______ students is a girl, a senior, or both.

Problem 1:Determine if events A and B are independent, P(B) = P(B|A). We are given that P(B) = 1/5. We need to find P(B|A).

P(B|A)=P(AandB)/P(A) = 2/25_______=2/25*5/2=________.

P(B)=P(B|A)so the events are __________.

Problem 2:Determine if events A andB are independent ifP(A)= 3/4, P(B) =3/10, and P(A and B) = 3/40.

If events A and B are independent, P(B) = P(B|A).

We are given that P(B) = 3/10. We need to find P(B}A).

P(B|A) = P(A and B)/P(A)=______3/4=3/10*4/3=________

P(B)P(B|A) so the events are ______________.

Suppose we have bag of balls (3 red, 2 yellow, and 1 blue) and we want to find the probability of randomly picking two red balls. We will replace the first ball before we choose the second one.

Are we choosing one item or more than one item? ________

The multiplication rule isP(RedandRed)=P(R)P(R|R)

First, determine if the events are dependent or independent by comparingP(R) andP(R|R)

P(R), is the probability of choosing a red ball without any conditions. There are_____ red balls out of a total of ______ balls in the bag so P(R) = 3/6=1/2.

Now let's put that ball back in the bag and choose again. What is the probability of choosing a red ball, given that the first ball that we chose was red,P(R|R)?

Since we put the red ball back in the bag, we still have 3 red balls out of a total of 6 balls, soP(R|R)=______

SinceP(R)=P(R|R) we know the events are______________.

Now, let's find the probability of choosing two red balls, but this time, we will not put the first ball back into the bag.

Are we choosing one item or more than one item? _________

Determine if the events are dependent or independent by comparingP(R) andP(R|R).We start out with 3 red balls out of 6 total balls, soP(R)=3/6=1/2 when there are no conditions.Since we do not replace the ball that we chose, we have one less ball in the bag for our second pick.

This time we have ____ red balls out of a total of _____ balls, so P(R|R) = 2/5.

P(R) ________ P(R|R) is equal to or not equal to

P(Red and Red) = P(R) * (P)R|R) = 1/2*2/5=2/10=_______

The probability of choosing a red ball, keeping it, and then choosing another red ballis 1/5 or _____%.

Using the same bag of 6 balls (3 red, 1 blue, 2 yellow), what is the probability of choosing a red ball, keeping it, and then choosing a blue ball?

The events choosing a red ball and choosing a blue ball are ________ (dependent or independent)

P(red and blue) = ________

Determine if the events are independent or dependent.

Problem 1

Tweets (T) | Do not Tweet (N )| Total

Male (M) 106 294 400

Female (F) 53 147 200

Total 159 441 600

P(T|M) ______(equals/does not equal) P(T) and P(M|T) ______(equals/does not equal) P(M) so the events Tweets and Male are _______(independent/dependent)

Problem 2

Prefers burgers | Prefers dogs (D) | Total

Prefers soda (S) 56 45 101

Prefers water (W) 67 34 101

Total 123 79 202

P(H|W) __________ (equal/does not equal) P(H) and P(W|H) ________(equal/does not equal) so the events are ____________(dependent/independent)

There are 52 cards in a deck. Twenty-six cards are black and 26 cards are red. The 52 cards can be broken down into four different suits; 13 hearts (), 13 diamonds (), 13 clubs (), and 13 spades (). Each card in a suit are labeled A (ace), 2-10, J (jack), Q (queen), and K (king). There are NO Jokers in a standard deck.Jacks, queens, and kings can also be called face cards.

Determine if you should use the addition rule or the multiplication rule. If you should use the addition rule, determine if the events are mutually exclusive. If you should use the multiplication rule, determine if the events are dependent or independent.

Problem 1:What is the probability of choosing a jack?

Is this a simple or a compound probability? ________

How many cards are being drawn? _______

Is this a conditional probability? _________

P(J) = the number of __________ number of cards = _____/52=______

Problem 2:What is the probability of choosing an ace of spades?(NOTE:This could also say, "What is the probability of drawing one card that is spade, given that it is an ace?"

Is this a simple or a compound probability? _______

How many cards are being drawn? _______

P(Ace of Spades) = P(S|A) = _____

Problem 3:What is the probability of choosing a 4 or a spade?

Is this a simple or a compound probability?______________

How many cards are being drawn?________

The conjunction used is ______ (or/and) so we should _______(add/multiply)

P(4 or spade) = 4/52+13/52 - (_____52) = ______

Problem 4:What is the probability of choosing a 7 and a 3 (with replacement)?

Is this a simple probability or a compound probability?___________

How many cards are being drawn? __________(more than one/one)

The conjunction used is _______(and/or) so we should ______(add/multiply)

The events drawing a 7 and drawing a 3 are _________(mutually exclusive/not mutually exclusive/ independent/independent)

P(7and3)=

P(7 and 3) = 4/52 ____ ______ = _________

Problem 5:What is the probability of choosing an Ace and an 8 (without replacement)?

Is this a simple probability of a compound probability?_______________

How many cards are being drawn? ________________(more than one/one)

The conjunction used is ________ so we should ___________

The events drawing an ace and drawing an 8 are ____________(dependent/independent)

P(A and 8) = 4/52 _____ ______ = _______

Problem 6:Now, find the following probabilities

What is the probability of drawing a king, replacing it, and then another king? P(K and K) =

What is the probability of drawing a black or a red card?__________ = __________

What is the probability of drawing a red queen, keeping it, and then drawing a black queen? ___________

What is the probability of drawing a king, keeping it, and then drawing another king? P(K___(and/or) K)= _______

What is the probability of drawing a heart?P( _____) = __________

What is the probability of drawing a face card (jack, queen, or queen)?P(F)= ___________

What is the probability of drawing an ace, a 2, and a 3, without replacement?P(A ____ (and/or) 2 ____(and/or) 3) = ___________

What is the probability of drawing a Club or a 7?P(C ____ (and/or) 7) = _________

What is the probability of drawing an ace, a 2 or a 3?P(A ____(and/or) 2 (and/or) 3) = _____________