Question

Find the possible outcomes for each event in rolling a number die. Then find the probability of each event as a fraction, decimal and percent.

Answer 1

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

STEP 1: Write the formula for calculating probability

`P(event)=\frac{number\text{ of favorable outcomes}}{number\text{ of possible outcomes}}`

STEP 2: State the number of possible outcomes

`\begin{gathered} A\text{ die has 6 faces numbered 1,2,3,4,5,6} \\ Therefore,\text{ the number of possible outcomes will be 6} \end{gathered}`

STEP 3: Answer question A

Rolling a number less than 7

`\begin{gathered} Numbers\text{ less than 7}\Rightarrow6,5,4,3,2,1 \\ n(numbers\text{ less than 7\rparen}\Rightarrow6 \\ \\ By\text{ substituting the values into the formula in step 1,} \\ P(Rolling\text{ a number less than 7\rparen}\Rightarrow(6)/(6)=1 \\ \\ Percentage\Rightarrow(1)/(1)*100=100\% \end{gathered}`

Hence,

Possible outcomes are 6,5,4,3,2,1

Probability = 1

Probability = 1.0 as decimal

Probability = 100% as percentage

STEP 4: Answer Question B

Rolling an 8

`\begin{gathered} Possible\text{ outcomes}\Rightarrow8 \\ n(8)\Rightarrow0 \\ Probability=(0)/(8)=0 \\ Percentage=0*100\%=0\% \end{gathered}`

Hence,

Possible outcome is 0 since there is no face of the die having 8

Probability = 0

Probability = 0.0 as decimal

Probability = 0% as percentage

STEP 5: Answer Question C

Rolling a number greater than 4

`\begin{gathered} Possible\text{ Outcomes}\Rightarrow5,6 \\ n(Possible\text{ outcomes\rparen}\Rightarrow2 \\ Probability=(2)/(6)=(1)/(3)\approx0.333 \\ Percentage=(1)/(3)*100=(100)/(3)=33.33\% \end{gathered}`

Hence,

Possible outcomes are 5,6

Probability = 1/3

Probability = 0.333 as decimal

Probability = 33.33% as percentage

STEP 6: Answer Question D

Rolling a number other than 6

`\begin{gathered} Possible\text{ outcomes}\Rightarrow1,2,3,4,5 \\ n(Possible\text{ outcomes\rparen}\Rightarrow5 \\ Probability=(5)/(6)=0.8333 \\ Percentage=(5)/(6)*100=83.33\% \end{gathered}`

Hence,

Possible outcomes are 1,2,3,4,5

Probability = 5/6

Probability = 0.8333 as decimal

Probability = 83.33% as percentage