Questions for Finite Math sections 7.1, 7.2, and 7.3

7.1 questions 1,5,11,23,24, and 25 - Dice, Die Rolls, Sales of Hybrid Vehicles

In the exercises below describe the sample space S of the experi-ment, and list the elements of the given event. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.)

#1 - Two coins are tossed; the result is at most one tail.

#5 - Two distinguishable dice are rolled; the numbers add to 5.

#11 - A letter is chosen at random from those in the word Mozart; the letter is a vowel.

Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 11. In the exercises below express the stated event in symbolic form and say how many elements it contains.

#23 - The red die shows 1, and the numbers add to 4.

#24 - The red die shows 1, but the numbers do not add to 11.

#25 - The numbers do not add to 4.

7.2 questions 7,8,9,10,13,14, and 15 - Dice, Die Rolls, Sales of Hybrid Vehicles

The exercises below are based on the following table, which shows the frequency of outcomes when two distinguishable coins were tossed 4,000 times and the uppermost faces were observed.

Outcome	HH	HT	TH	TT
Frequency	1,100	950	1,200	750

#7 - Determine the relative frequency distribution.

#8 - What is the relative frequency that heads comes up at least once?

#9 - What is the relative frequency that the second coin lands with heads up?

#10 - What is the relative frequency that the first coin lands with heads up?

In the exercises below say whether the given distribution can be a relative frequency distribution. If your answer is no, indicate why not.

#13 -

Outcome	1	2	3	5
Rel. Frequency	.4	.6	0	0

#14 -

Outcome	A	B	C	D
Rel. Frequency	.2	.1	.2	.1

#15 -

Outcome	HH	HT	TH	TT
Rel. Frequency	.5	.4	.5	-.4

7.3 questions 1 and 2 parts a,b,c, and d - Probability of Unions, Intersections, Complements, and Probability Distribution Table

Complete the following probability distribution table, and then calculate the stated probabilities.

Outcome	a	b	c	d	e
Probability	.1	.05	.6	.05

#1a - P({a, c, e)}

#1b - P(E U F), where E = {a, c, e} and F = {b, c, e}

#1c - P(E'), where E is as in part (b)

#1d - P(E F), where E and F are as in part (b)

Repeat Exercise 1 using the following table.

Outcome	a	b	c	d	e
Probability	.1		.65	.1	.05

#2a - P({a, c, e)}

#2b - P(E U F), where E = {a, c, e} and F = {b, c, e}

#2c - P(E'), where E is as in part (b)

#2d - P(E F), where E and F are as in part (b)