Statistics

David Freedman, Robert Pisani, Roger Purves

Chapter 13

What Are the Chances? - all with Video Answers

Educators

Chapter Questions

Problem 1

True or false, and explain:
(a) If something has probability 1,000 $\%$ , it is sure to happen.
(b) If something has probability 90$\%$ , it can be expected to happen about nine times as often as its opposite.

Bryan Luo

Bryan Luo

Numerade Educator

Problem 2

Two cards will be dealt off the top of a well-shuffled deck. You have a choice:
(i) To win $\$ 1$ if the first is a king.
(ii) To win $\$ 1$ if the first is a king and the second is a queen.Which option is better? Or are they equivalent? Explain briefly.

Heena Haldankar

Heena Haldankar

Numerade Educator

Problem 3

Four cards will be dealt off the top of a well-shuffled deck. There are two options:
(i) To win $\$ 1$ if the first card is a club and the second is a diamond and the third is a heart and the fourth is a spade.
(ii) To win $\$ 1$ if the four cards are of four different suits.
Which option is better? Or are they the same? Explain.

Bryan Luo

Numerade Educator

Problem 4

A poker hand is dealt. Find the chance that the first four cards are aces and
the fifth is a king.

Heena Haldankar

Heena Haldankar

Numerade Educator

Problem 5

One ticket will be drawn at random from the box below. Are color and number independent? Explain.

Bryan Luo

Numerade Educator

Problem 6

A deck of cards is shuffled and the top two cards are placed face down on a table. True or false, and explain:
(a) There is 1 chance in 52 for the first card to be the ace of clubs.
(b) There is 1 chance in 52 for the second card to be the ace of diamonds.
(c) The chance of getting the ace of clubs and then the ace of diamonds. 1$/ 52 \times 1 / 52$ .

Heena Haldankar

Heena Haldankar

Numerade Educator

Problem 7

A coin is tossed six times. Two possible sequences of results are
(i) HTTHTH (ii) HHHHH
(The coin must land $\mathrm{H}$ or $\mathrm{T}$ in the order given $; \mathrm{H}=$ heads $, \mathrm{T}=$ tails. $)$ Which of the following is correct? Explain.
(a) Sequence (i) is more likely.
(b) Sequence (ii) is more likely.
(c) Both sequences are equally likely.

Bryan Luo

Numerade Educator

Problem 8

A die is rolled four times. What is the chance that-
(a) all the rolls show 3 or more spots?
(b) none of the rolls show 3 or more spots?
(c) not all the rolls show 3 or more spots?

Heena Haldankar

Heena Haldankar

Numerade Educator

Problem 9

A die is rolled 10 times. Find the chance of $-$
(a) getting 10 sixes.
(b) not getting 10 sixes.
(c) all the rolls showing 5 spots or less.

Bryan Luo

Numerade Educator

Problem 10

Which of the two options is better, or are they the same? Explain briefly.
(i) You toss a coin 100 times. On each toss, if the coin lands heads, you win $\$ 1 .$ If it lands tails, you lose $\$ 1 .$
(ii) You draw 100 times at random with replacement from $\lfloor\square[0]$ each draw, you are paid (in dollars) the number on the ticket.

Heena Haldankar

Heena Haldankar

Numerade Educator

Problem 11

In the box shown below, each ticket should have two numbers:
A ticket will be drawn at random. Can you fill in the blanks so the two numbers are independent?

Bryan Luo

Numerade Educator

Problem 12

You are thinking about playing a lottery. The rules: you buy a ticket, choose 3 different numbers from 1 to $100,$ and write them on the ticket. The lottery has a box with 100 balls numbered from 1 through $100 .$ Three balls are drawn at random without replacement. If the numbers on these balls are the same as
the numbers on your ticket, you win. (Order doesn't matter.) If you decide to play, what is your chance of winning?

Heena Haldankar

Heena Haldankar

Numerade Educator