Which event is most likely to occur? $\newline$ Rolling a number greater than $4$ on a twelve-sided die, numbered from $1$ to $12$ . $\newline$ Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on green or purple. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $48$ tickets. $\newline$ Reaching into a bag full of $52$ strawberry chews and $8$ cherry chews without looking and pulling out a strawberry chew.

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Algebra 1

Solve a system of equations using elimination: word problems

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Q. Which event is most likely to occur?

\newline

Rolling a number greater than

4

on a twelve-sided die, numbered from

1

12

\newline

Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on green or purple.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

48

tickets.

\newline

Reaching into a bag full of

52

strawberry chews and

8

cherry chews without looking and pulling out a strawberry chew.

Calculate Probability Twelve-Sided Die: Calculate the probability of rolling a number greater than $4$ on a twelve-sided die. $\newline$ There are $12$ possible outcomes when rolling a twelve-sided die. The numbers greater than $4$ are $5, 6, 7, 8, 9, 10, 11,$ and $12$ . There are $8$ numbers greater than $4$ . $\newline$ Probability = Number of favorable outcomes / Total number of outcomes $\newline$ Probability = $\frac{8}{12}$ $\newline$ Probability = $\frac{2}{3}$
Calculate Probability Spinner: Calculate the probability of spinning green or purple on the spinner. $\newline$ There are $5$ equal-sized sections, so there are $5$ possible outcomes. Green and purple are two of the outcomes. $\newline$ Probability $=$ Number of favorable outcomes $/$ Total number of outcomes $\newline$ Probability $= \frac{2}{5}$
Calculate Probability Raffle: Calculate the probability of winning the raffle with $48$ tickets. $\newline$ There are $100$ tickets sold in total, and you have $48$ of them. $\newline$ Probability = Number of favorable outcomes / Total number of outcomes $\newline$ Probability = $\frac{48}{100}$ $\newline$ Probability = $0.48$
Calculate Probability Strawberry Chew: Calculate the probability of pulling out a strawberry chew from the bag. $\newline$ There are $52$ strawberry chews and $8$ cherry chews, making a total of $60$ chews. $\newline$ Probability = Number of favorable outcomes / Total number of outcomes $\newline$ Probability = $\frac{52}{60}$ $\newline$ Probability = $\frac{13}{15}$
Compare Probabilities: Compare the probabilities to determine which event is most likely to occur. $\newline$ The probabilities are: $\newline$ Rolling a number greater than $4$ on a twelve-sided die: $\frac{2}{3}$ $\newline$ Spinning green or purple: $\frac{2}{5}$ $\newline$ Winning the raffle: $0.48$ $\newline$ Pulling out a strawberry chew: $\frac{13}{15}$ $\newline$ The highest probability is the one closest to $1$ .
Identify Highest Probability: Identify the event with the highest probability. $\newline$ The probability of pulling out a strawberry chew is $\frac{13}{15}$ , which is approximately $0.867$ . $\newline$ This is higher than the probability of rolling a number greater than $4$ on a twelve-sided die ( $\frac{2}{3}$ or approximately $0.667$ ), spinning green or purple ( $\frac{2}{5}$ or $0.4$ ), and winning the raffle ( $0.48$ ). $\newline$ Therefore, pulling out a strawberry chew is the most likely event.