Question

. Betty has several of the standard six-sided dice that are common in many board games. If Betty rollsone of these dice, what is the probability that:A: She rolls a three. (enter the answer as a percent rounded to the nearest tenths place)B: She rolls a six. (enter the answer as a percent rounded to the nearest tenths place)C: She rolls a three or a six. (enter the answer as a percent rounded to the nearest tenths place)D: She rolls an even number (enter the answer as a percent rounded to the nearest tenths place

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for probability

`Probability=\frac{number\text{ of required outcomes}}{number\text{ of total outcomes}}`

STEP 2: Wit the required data

`\begin{gathered} For\text{ a standard six-sided die,} \\ The\text{ total outcomes is 6} \\ n(Total)=6 \end{gathered}`

STEP 3: Find the probability that she rolls a three

`\begin{gathered} n(3)=1 \\ n(total)=6 \\ Pr(3)=(1)/(6) \\ To\text{ percentage:} \\ (1)/(6)*100=16.6666667\approx16.7\% \end{gathered}`

The probability that she rolls a three is 16.7%

STEP 4: Find the probability that she rolls a six

The probability that she rolls a six is 16.7%

STEP 5: Find the probability that she rolls three or a six

`\begin{gathered} Pr(3\text{ or 6\rparen}=Pr(3)+Pr(6) \\ =(1)/(6)+(1)/(6)=(2)/(6)=(1)/(3) \\ To\text{ percentage''} \\ (1)/(3)*100=(100)/(3)=33.3333333\approx33.3\% \end{gathered}`

The probability that she rolls a three or six is 33.3%

STEP 6: Find the probability that she rolls an even number

`\begin{gathered} Even\text{ number}=2,4,6 \\ n(even\text{ number\rparen}=3 \\ Pr(even\text{ number\rparen}=(3)/(6)=(1)/(2) \\ To\text{ percentage:} \\ (1)/(2)*100=(100)/(2)=50\% \end{gathered}`

The probability that she rolls an even number is 50.0%