 Page  Complete Assessment

 The following represents the body temperatures of healthy students Find the average temperature. (tenths) 2. Find the standard deviation. (tenths) 3. What percent of the students have a temperature below ? 4. What percentage is between and 99.33?

 The following represents the body temperatures of healthy students Find the average temperature. (tenths) (98.37) 2. Find the standard deviation. (tenths) (0.96) 3. What percent of the students have a temperature below ? (97.5) 4. What percentage is between and 99.33? (81.5)

 Part over Whole SHORT RESPONSE Of the 32 students in class, 22 own dogs, 17 own cats, and 8 own birds. Nine students own dogs only, 7 own cats only, and 2 own birds only. One student owns a dog, a cat, and a bird. Eight students own a cat and a dog, but not a bird. One student owns a cat and a bird, but not a dog. If a student is selected at random, what is the probability that the student owns a dog and a bird, but not a cat? There are 22 students who own dogs, so there are 22 – 9 – 8 – 1 = 4 students who own a dog and a bird, but not a cat.

 Independent  Outcome of first event does not affect outcome of second.  Dependent  Outcome of first event does affect outcome of second.  Mutually Exclusive  Events that cannot occur at the same time are called mutually exclusive.  Inclusive  If two events are not mutually exclusive, they are called inclusive.  Conditional  Probability of a second dependent event occurring assuming the first has already occurred.

 Exclusive: Mutually Exclusive: can't happen at the same time  Tossing a coin: Heads and Tails are Mutually Exclusive  Cards: Kings and Aces are Mutually Exclusive  The probability of A or B is the sum of the individual probabilities:  P(A or B) = P(A) + P(B)  "The probability of A or B equals the probability of A plus the probability of B"  Example: In a Deck of 52 Cards: the probability of a King is 1/13, so P(King)=1/13 and the probability of an Ace is also 1/13, so P(Ace)=1/13. When we combine those two Events: The probability of a card being a King or an Ace is (1/13) + (1/13) = 2/13

 NOT Exclusive (where there is overlap). P(A or B) = P(A) + P(B) - P(A and B). "The probability of A or B equals the probability of A plus the probability of B minus the probability of A and B."  Example: Hearts and Kings. In a deck of cards, only the King of Hearts is a Heart and a King. But Hearts or Kings is all the Hearts (13 of them) all the Kings (4 of them) But that counts the King of Hearts twice! So the opportunity to draw Hearts or Kings would include 16 Cards = 13 Hearts + 4 Kings - the 1 extra King of Hearts.

TRAVEL Rae is flying from Birmingham to Chicago on a flight with a 90% on-time record. On the same day, the chances of rain in Denver are predicted to be 50%. What is the probability that Rae’s flight will be on time and that it will rain in Denver? P(A and B)= P(A) ● P(B) P(on time and rain) = P(on time) ● P(rain) = 0.9 ● 0.5 = 0.45 The probability that Rae’s flight will be on time and that it will rain in Denver is 45%.

 are not affected by previous events. The toss of a coin and throwing dice are all examples of random events. You can calculate the chances of two or more independent events by multiplying the chances. P(A and B) = P(A) × P(B). Example: what is the probability of getting a "Head" when tossing a coin? ½. The probability of getting 2 “Heads” in a row is ½ * ½ or ¼.

 are affected by what happened before, Example: taking colored marbles from a bag: as you take each marble there are less marbles left in the bag, so the probabilities change. For multiple dependent events, you multiply the probabilities of each event, adjusting for the ongoing changes. If you start with a bag of 10 marbles, where 5 are red, the probability of drawing a red marble is 5/10. The chances of drawing 2 red marbles is 5/10 * 4/9 = 20/90 or 2/9.   This is referred to as Conditional Probability. "The probability of event B given event A equals the probability of event A and event B divided by the probability of event A.” Rolling a six-sided die, what is the probability that if you rolled a 2 or 4 given that you rolled an even number? Let event A be that she rolled an even number. Let event B be that she rolled a 2 or 4. P(A) =. Three of the six outcomes are an even number. P(A and B) Two of the six outcomes is 2 or 4.  P(B | A) =  Probability of B given A. ( 2/6  1/2 = 2/6*2/1) = 4/6 or 2/3

A. GAMES At the school carnival, winners in the ring-toss game are randomly given a prize from a bag that contains 4 sunglasses, 6 hairbrushes, and 5 key chains. Three prizes are randomly drawn from the bag and not replaced. Find P(sunglasses, hairbrush, key chain). First prize: Third prize: Second prize: P(sunglasses, hairbrush, key chain) = P(sunglasses) ● P(hairbrush) ● P(key chain)

A card is being drawn from a standard deck. Find the probability of P(7 or 8). ← ← ← ← P(7 or 8)= P(7) + P(8)Probability of mutually exclusive events. Answer: The probability of drawing a 7 or 8 is or about 15.4%.

GAMES In the game of bingo, balls or tiles are numbered 1 through 75. These numbers correspond to columns on a bingo card, as shown in the table. A number is selected at random. What is the probability that it is a multiple of 5 or is in the N column? P(multiple of 5) P(N column) P(multiple of 5 and N column) = = =

 Brain Pop Brain Pop

 Start with the number of variables in the expression 7x 2 y.  Multiply by the exponent on the variable in 4a 4.  Take the cube root of your answer.  Take 250% of your answer  Square your answer

Kim draws a card from a standard 52-card deck. What is the probability that she draws a heart given that the card is from a red suit? There are 26 red cards in a deck. There are 13 hearts. Let event A be that she drew a red card. Let event B be that she drew a heart. 26 of the 52 cards are of a red suit. 13 of the 52 cards are of a red suit and a heart The probability of drawing a card that was a heart given that the card is from a red suit is 50%.

Vitali draws a card from a standard 52-card deck. What is the probability that she draws a Jack given that the card she drew is a face card? A. B. C. D.

 COLLEGE Find the probability that a student plans to attend college after high school if the student is a girl. There is a total of or 1007 people in the study. We need to find the probability of girls planning to attend college after high school. Conditional Probability Formula

The table shows the number of students who are varsity athletes. Find the probability that a student is non-varsity given that he or she is a senior. A16.6% B19.8% C50.4% D83.4%

 14-3 Worksheet (odd problems)  Page – 21 (odd)

 13 1/13  15. 1/3  17. 6/37  19 25/67 and  21.2*.4*.25 = 2%

1. A gumball machine contains 16 red gumballs, 10 blue gumballs, and 18 green gumballs. Once a gumball is removed from the machine, it is not replaced. Find each probability if the gumballs are removed in the order indicated. P(green, blue, not red) A. B. C. D. 2. In Mrs. Kline’s class, 7 boys have brown eyes and 5 boys have blue eyes. Out of the girls, 6 have brown eyes and 8 have blue eyes. If a student is chosen at random from the class, what is the probability that the student will be a boy or have brown eyes? A. B. C. D.

A.6.5% B.7.1% C.7.7% D.8.4% 3. The table shows the number of students who are varsity athletes. Find the probability that a student is varsity given that he or she is a sophomore. 4. The French Club has 16 seniors, 12 juniors, 15 sophomores, and 21 freshmen as members. What is the probability that a member chosen at random is a junior or a senior? A. B.1 C. D.0

1. A gumball machine contains 16 red gumballs, 10 blue gumballs, and 18 green gumballs. Once a gumball is removed from the machine, it is not replaced. Find each probability if the gumballs are removed in the order indicated. P(green, blue, not red) A. B. C. D. 2. In Mrs. Kline’s class, 7 boys have brown eyes and 5 boys have blue eyes. Out of the girls, 6 have brown eyes and 8 have blue eyes. If a student is chosen at random from the class, what is the probability that the student will be a boy or have brown eyes? A. B. C. D.

A.6.5% B.7.1% C.7.7% D.8.4% 3. The table shows the number of students who are varsity athletes. Find the probability that a student is varsity given that he or she is a sophomore. 4. The French Club has 16 seniors, 12 juniors, 15 sophomores, and 21 freshmen as members. What is the probability that a member chosen at random is a junior or a senior? A. B.1 C. D.0