Page 163 - NUMINO Challenge_D2

Answer
Key

Therefore, the game can be fair if the entry fee 12 Coloring p.102~103
is $4, but since it was $5, the game is unfair.
Example 2 2, B 2, 2, 12
2 The game needs to be played at least three
Example 1
times before it is ended. During the game, when 23
the coin is flipped for the second time and third
time, the outcomes of having the number side 1 2
and picture side are as shown below. (Let 2 1
represents the number side and represent the
picture side.)

First Second Third

A wins 1 2, 1, 2 2 3
A wins
A wins
B wins

There are three outcomes in which A wins, and Type 12-1 The Number of Ways to Color p.104~105

one outcome in which B wins. Therefore, it is fair 12
2 2 colors
that A gets 24 3 18 coins and B gets 3 3 colors
24 4 4 4 3 2 2 3 144 ways
1
4 6 coins.

3 Let represents a black marble and , , and Problem solving

represent each of the three white marbles. 1 If the snowman is colored in the order of A, B,
The outcomes of taking out two marbles are as
shown below. C, and D, the number of colors that can be used
for each part is 4, 3, 2, and 3.
,,,,, Therefore, there are 4 3 2 3 72 ways to
In these outcomes, the possibility of having the color the snowman.
same color or different colors is the same.
Therefore, it will be fair to pay 15 2 7.50 2 Let , , , , and represent each part.
dollars.

4 From the 100 outcomes of having one marble,

there is only one outcome of having only 300
dollars. Therefore, the value of one marble is
300 100 3 dollars.

There are 3 ways to color .
There are 2 ways to color besides the ways
used for . There is 1 way to color besides
the ways used for and . There is 1 way to
color besides the ways used for and .
Since there is 1 way to color besides the ways
used for and , there are 3 2 1 1 1 6
ways to color the envelope.

NUMINO Challenge D2