Which event is least likely to occur? $\newline$ Rolling a number greater than or equal to $6$ on a eight-sided die, numbered from $1$ to $8$ . $\newline$ Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on yellow. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $79$ tickets. $\newline$ Reaching into a bag full of $75$ strawberry chews and $5$ 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 least likely to occur?

\newline

Rolling a number greater than or equal to

6

on a eight-sided die, numbered from

1

8

\newline

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

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

79

tickets.

\newline

Reaching into a bag full of

75

strawberry chews and

5

cherry chews without looking and pulling out a strawberry chew.

Calculate Probability of Rolling: Calculate the probability of rolling a number greater than or equal to $6$ on an eight-sided die. $\newline$ There are $3$ favorable outcomes ( $6$ , $7$ , $8$ ) out of $8$ possible outcomes. $\newline$ Probability = Number of favorable outcomes / Total number of outcomes $\newline$ Probability = $\frac{3}{8}$
Calculate Probability of Spinning: Calculate the probability of spinning the spinner and landing on yellow. $\newline$ There is $1$ favorable outcome (yellow) out of $4$ possible outcomes. $\newline$ Probability = $\frac{1}{4}$
Calculate Probability of Winning: Calculate the probability of winning the raffle after buying $79$ tickets out of $100$ . There are $79$ favorable outcomes out of $100$ possible outcomes. Probability = $\frac{79}{100}$
Calculate Probability of Pulling: Calculate the probability of pulling out a strawberry chew from the bag. $\newline$ There are $75$ favorable outcomes (strawberry chews) out of $80$ total chews ( $75$ strawberry + $5$ cherry). $\newline$ Probability = $\frac{75}{80}$ $\newline$ Probability = $\frac{15}{16}$ (simplified)
Compare Probabilities: Compare the probabilities to determine the least likely event. $\newline$ Rolling a number greater than or equal to $6$ : $\frac{3}{8} = 0.375$ $\newline$ Spinning and landing on yellow: $\frac{1}{4} = 0.25$ $\newline$ Winning the raffle: $\frac{79}{100} = 0.79$ $\newline$ Pulling out a strawberry chew: $\frac{15}{16} = 0.9375$ $\newline$ The event with the smallest probability is the least likely to occur.
Identify Smallest Probability: Identify the event with the smallest probability. The smallest probability is $\frac{1}{4}$ , which is the probability of spinning the spinner and landing on yellow.