Question

chapter 4 probability and odds 171
chapter test

1. complete the following table showing the alternative ways of expressing a probability.

ways of expressing probability

fraction	decimal	percentage	words
	0.23
			1 out of 16
		94%

1. the playing pieces in a board game include a bag of 30 red chips, 20 blue chips, and 15 yellow chips.

a) if danica randomly chooses a chip from the bag, what is the probability that it will be yellow?
b) what are the odds in favour of danica choosing a yellow chip?
c) danica does draw a yellow chip, does not return it to the bag, then passes the bag to ahmet. what are the odds in favour of ahmet drawing a blue chip?
board games have existed since ancient egypt. board games nowadays typically have a counter or game piece that moves along the playing board. a die or dice are rolled to move game pieces and provide an element of chance.

Explanation:

Step1: Convert $\frac{3}{125}$ to decimal

$3\div125 = 0.024$

Step2: Convert 0.024 to percentage

$0.024\times100\%=2.4\%$, words: 3 out of 125

Step3: Convert 0.23 to fraction

$0.23=\frac{23}{100}$, to percentage: $0.23\times 100\% = 23\%$, words: 23 out of 100

Step4: Convert 1 out of 16 to fraction

$\frac{1}{16}$, to decimal: $1\div16 = 0.0625$, to percentage: $0.0625\times100\% = 6.25\%$

Step5: Convert 94% to fraction

$\frac{94}{100}=\frac{47}{50}$, to decimal: $94\div100 = 0.94$, words: 94 out of 100

Step6: Calculate probability of yellow - chip in part a

Total chips: $30 + 20+15=65$. Probability of yellow chip $P=\frac{15}{65}=\frac{3}{13}\approx0.2308\approx23.08\%$

Step7: Calculate odds in favor of yellow - chip in part b

Odds in favor of an event $E$ is $\frac{P(E)}{1 - P(E)}$. $P(E)=\frac{3}{13}$, $1 - P(E)=\frac{10}{13}$. Odds in favor $=\frac{3}{10}$ or 3:10

Step8: Calculate odds for Ahmet in part c

After Danica draws a yellow chip, total chips left: $65 - 1=64$, blue chips: 20. Probability of blue chip $P=\frac{20}{64}=\frac{5}{16}$, $1 - P=\frac{11}{16}$. Odds in favor $=\frac{5}{11}$ or 5:11

Answer:

Fraction	Decimal	Percentage	Words
$\frac{23}{100}$	0.23	23%	23 out of 100
$\frac{1}{16}$	0.0625	6.25%	1 out of 16
$\frac{47}{50}$	0.94	94%	94 out of 100

a. $\frac{3}{13}$
b. 3:10
c. 5:11