Algebra 2
Review for Unit 14 Test Name:
1) If P(E) is the probability that an event will occur, then which of the following is true? (1) 0 P(E) 1 (3) 0 P(E) 1
(2) 0 P(E) 1 (4) 0 P(E) 1
2) From a standard deck of 52 cards, one card is drawn and, without replacement, a second card is drawn. What is the probability that both cards are black jacks?
3) In a standard deck of 52 cards, what is the probability of drawing a black card or a 7?
4) The probability that you will solve any given math problems correctly is 0.91. Find the probability that you will solve 3 randomly selected math problems correctly.
5) A fair coin is flipped twice and the result is noted each time.
a) Draw a tree diagram to show all of the different outcomes in the sample space.
b) List all of the outcomes as ordered pairs. How many of them are there?
c) Find each of the following probabilities:
6) A blood collection agency tests 50 blood samples to see what type they are. Their results are shown in the table below.
(a) If a blood sample is picked at random, what is the probability it will be type AB?
(b) If a blood sample is picked at random, what is the probability it will not be type A?
(c) Are the two probabilities you calculated in parts a and b theoretical or empirical? Explain your choice.
7) Sal has a small bag of candy containing four yellow candies and three blue candies. While waiting for the bus, he ate two candies out of the bag, one after another, without looking. What is the probability that both candies were the same color?
8) Emily and Katie both play soccer. The probability that Emily will score a goal on her first attempt is 0.32. The probability that Kate will score a goal on her first attempt is 0.75. Calculate the probability that
(a) Emily and Katie will both score a goal on their first attempts;
9) The table below shows the number of left and right handed tennis players in a sample of 50 males and females.
Left handed Right handed Total
Male 3 29 32
Female 2 16 18
Total 5 45 50
If a tennis player was selected at random from the group, find the probability that the player is (a) female and right handed;
(b) left handed;
(c) right handed, given that the player selected is male.
10) Events A and B are independent. Suppose ( ) ( ) ( )
12) The seniors from Harrison High School are required to participate in exactly one after-school sport. Data were gathered from a sample of 120 students regarding their choice of sport. The following data were recorded.
(a) For this group of students, do these data suggest that gender and sports are independent of each other? Justify your answer.
(b) Two students are chosen at random from 120 students. Find the probability that: (i) both play tennis;
(ii) neither play football;
13) When a room is randomly selected in a downtown hotel, the probability that the room has a
kitchenette is , the probability that the room has waterfront view is , and the probability that it has a kitchenette and a view of the water is . Let be the event that the room has a kitchenette, and let be the event that the room has a waterfront view.
a. What is the meaning of ( ) in this context?
b. Use a hypothetical 1000 table to calculate ( ).
(room has a kitchenette)
Not
(room does not have a kitchenette)
Total
(room has a view of the water)
Not
(room does not have a view
of the water) Total
c. There is also a formula for calculating a conditional probability. The formula for conditional probability is
( ) ( ) ( )
Use this formula to calculate ( ), where the events and are as defined in this example.
14) There are 32 students in a science class. Twelve of these students belong to the Math Club, 20 students belong to the Chemistry Club, and 9 students belong to both.
a) Draw a Venn Diagram to represent this information.
b) How many students do not belong to either of these clubs?
c) What is the probability that the student belongs to both clubs?
15) In a sophomore class of 500 students, 95 students are in the ski club, 125 play intramural sports, and 30 of those students do both.
a) Draw a Venn Diagram to represent this information.
b) How many students are not involved in either ski club or intramural sports?
c) What is the probability that the student does not ski?
d) What is the probability that the student belongs to both clubs?
16) The table below describes the smoking habits of a group of asthma sufferers.
a) If one of the people is randomly selected, find the probability that the person is a woman or a regular smoker.
b) If one of the people is randomly selected, find the probability that the person is a non-smoker given that he is a man.
Nonsmoker Occasional Smoker
Regular Smoker
Heavy Smoker
Total
Men 344 40 85 39 508
Women 370 31 88 48 537
17) When a car is brought to a repair shop for a service, the probability that it will need the transmission fluid replaced is , the probability that it will need the brake pads replaced is , and the
probability that it will need both the transmission fluid and the brake pads replaced is . Let the event that a car needs the transmission fluid replaced be and the event that a car needs the brake pads replaced be .
a. What are the values of the following probabilities? i. ( )
ii. ( )
iii. ( )
b. Use the addition rule to find the probability that a randomly selected car needs the transmission fluid or the brake pads replaced.
18) A deck of cards consists of the following:
black cards showing squares, numbered – black cards showing circles, numbered – red cards showing X’s, numbered –
red cards showing diamonds, numbered –
A card will be selected at random from the deck.
a) Are the events “the card shows a circle” and “the card is red” disjoint? Explain.
b) Calculate the probability that the card will show a circle or will be red.
c) Are the events “the card shows a ” and “the card is black” disjoint? Explain.
