chapter 4 probability and odds 171\nchapter test\n1. complete the following table showing the alternative…

chapter 4 probability and odds 171\nchapter test\n1. complete the following table showing the alternative ways of expressing a probability.\nways of expressing probability\n|fraction|decimal|percentage|words|\n|----|----|----|----|\n|\\frac{3}{125}| | | |\n| |0.23| | |\n| | | |1 out of 16|\n| | |94%| |\n2. the playing pieces in a board game include a bag of 30 red chips, 20 blue chips, and 15 yellow chips.\na) if danica randomly chooses a chip from the bag, what is the probability that it will be yellow?\nb) what are the odds in favour of danica choosing a yellow chip?\nc) 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?\nboard 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.

chapter 4 probability and odds 171\nchapter test\n1. complete the following table showing the alternative ways of expressing a probability.\nways of expressing probability\n|fraction|decimal|percentage|words|\n|----|----|----|----|\n|\\frac{3}{125}| | | |\n| |0.23| | |\n| | | |1 out of 16|\n| | |94%| |\n2. the playing pieces in a board game include a bag of 30 red chips, 20 blue chips, and 15 yellow chips.\na) if danica randomly chooses a chip from the bag, what is the probability that it will be yellow?\nb) what are the odds in favour of danica choosing a yellow chip?\nc) 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?\nboard 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.

Answer

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
$\frac{3}{125}$ 0.024 2.4% 3 out of 125
$\frac{23}{100}$ 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