Chapter 14, More about Chance Video Solutions, Statistics

02:06

Problem 1

A pair of dice are thrown.

(a) Find the chance that both dice show 3 spots.
(b) Find the chance that both dice show the same number of spots.

Bryan Luo

Numerade Educator

02:02

Problem 2

In the game of Monopoly, a player rolls two dice, counts the total number of spots, and moves that many squares. Find the chance that the player moves 11 squares (no more and no less).

Heena Haldankar

Numerade Educator

03:44

Problem 3

True or false, and explain:

(a) Find the chance that both dice show 3 spots.
(b) Find the chance that both dice show the same number of spots.

Bryan Luo

Numerade Educator

04:34

Problem 4

Two cards will be dealt off the top of a well-shuffled deck. You have a choice:

(i) to win $\$ 1$ if at least one of the two cards is a queen.
(ii) to win $\$ 1$ if the first is a queen.
Which option is better? Or are they equivalent? Explain.

Heena Haldankar

Numerade Educator

01:11

Problem 5

The chance of $\mathrm { A }$ is $1 / 3 ;$ the chance of $\mathrm { B }$ is 1$/ 10 .$ True or false, and explain:

(a) If A and B are independent, they must also be mutually exclusive.
(b) If A and B are mutually exclusive, they cannot be independent.

Bryan Luo

Numerade Educator

02:32

Problem 6

One event has chance $1 / 2 ,$ another has chance 1$/ 3 .$ Fill in the blanks, using one phrase from each pair below, to make up two true sentences. Write out both sentences.

"If you want to find the chance that $\frac { ( i ) } { L }$ will happen, check to see if they are $\frac { ( \mathrm { ii } ) } { \longrightarrow } .$ If so, you can $\frac { ( \mathrm { iii } ) } { \longrightarrow }$ the chances."

(i) at least one of the two events, both events
(ii) independent, mutually exclusive

Heena Haldankar

Numerade Educator

02:47

Problem 7

Four draws are going to be made at random with replacement from the box $[ \square [ 2 ] [ 2 ] [ 3 ] [ 3 ]$ . Find the chance that $[ 2 ]$ is drawn at least once.

Bryan Luo

Numerade Educator

03:17

Problem 8

Repeat exercise $7 ,$ if the draws are made at random without replacement.

Heena Haldankar

Numerade Educator

02:00

Problem 9

One ticket will be drawn at random from each of the two boxes shown below:

$( \mathrm { A } ) \lfloor [ 1 ] [ 2 ] [ 3 ]$ $( \mathrm { B } ) \lfloor [ 1 ] [ 2 ] [ 3 ] [ 4 ]$

Find the chance that:
(a) The number drawn from A is larger than the one from B.
(b) The number drawn from A equals the one from B.
(c) The number drawn from A is smaller than the one from B.

Lynn Larson

Numerade Educator

03:17

Problem 10

There are two options:

(i) A die will be rolled 60 times. Each time it shows an ace or a six, you win $\$ 1 ;$ on the other rolls, you win nothing.
(ii) Sixty draws will be made at random with replacement from the box $[ [ 1 ] [ 1 ] [ 1 ] [ 0 ] [ 0 ] [ 0 ] ] .$ On each draw, you will be paid the amount shown on the ticket, in dollars.

Which option is better? or are they the same? Explain briefly.

Heena Haldankar

Numerade Educator

04:22

Problem 11

Three cards are dealt from a well-shuffled deck.

(a) Find the chance that all of the cards are diamonds.
(b) Find the chance that none of the cards are diamonds.
(c) Find the chance that the cards are not all diamonds.

Bryan Luo

Numerade Educator

02:19

Problem 12

A coin is tossed 10 times. True or false, and explain:

(a) The chance of getting 10 heads in a row is $1 / 1,024$ .
(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is 1$/ 2$ .

Heena Haldankar

Numerade Educator

04:02

Problem 13

A box contains 2 red marbles and 98 blue ones. Draws are made at random with replacement. In $\frac { \text { draws from the box, there is better than a } 50 \% } { \text { In } }$ chance for a red marble to appear at least once. Fill in the blank with the smallest number that makes the statement true. (You will need a calculator.)

Bryan Luo

Numerade Educator

05:13

Problem 14

In Lotto $6 - 53 ,$ there is a box with 53 balls, numbered from 1 to $53 .$ Six balls are drawn at random without replacement from the box. You win the grand prize if the numbers on your lottery ticket are the same as the numbers on the six balls; order does not matter.

Person A bought two tickets, with the following numbers:

$\begin{array} { l l l l l l l } { \text { Ticket } \# 1 } & { 5 } & { 12 } & { 21 } & { 30 } & { 42 } & { 51 } \\ { \text { Ticket } \# 2 } & { 5 } & { 12 } & { 23 } & { 30 } & { 42 } & { 49 } \end{array}$

Person B bought two tickets, with the following numbers:

$\begin{array} { l l l l l l l } { \text { Ticket } \# 1 } & { 7 } & { 11 } & { 25 } & { 28 } & { 34 } & { 50 } \\ { \text { Ticket } \# 2 } & { 9 } & { 14 } & { 20 } & { 22 } & { 37 } & { 45 } \end{array}$

Which person has the better chance of winning? Or are their chances the
same? Explain briefly.

Heena Haldankar

Numerade Educator