Which event is most likely to occur? $\newline$ Rolling a number greater than or equal to $3$ 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 blue or green. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $80$ tickets. $\newline$ Reaching into a bag full of $3$ strawberry chews and $57$ cherry chews without looking and pulling out a strawberry chew.

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Precalculus

Mean, variance, and standard deviation of binomial distributions

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Q. Which event is most likely to occur?

\newline

Rolling a number greater than or equal to

3

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 blue or green.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

80

tickets.

\newline

Reaching into a bag full of

3

strawberry chews and

57

cherry chews without looking and pulling out a strawberry chew.

Calculate Probability: Calculate the probability of rolling a number greater than or equal to $3$ on an eight-sided die. $\newline$ There are $8$ possible outcomes when rolling the die. The numbers greater than or equal to $3$ are $3, 4, 5, 6, 7,$ and $8$ . That's $6$ favorable outcomes. $\newline$ Probability $=$ Number of favorable outcomes $/$ Total number of outcomes $\newline$ Probability $= \frac{6}{8}$ $\newline$ Probability $= 0.75$
Spin Spinner: Calculate the probability of spinning the spinner and landing on blue or green. $\newline$ There are $4$ equal sections, so there are $4$ possible outcomes. The favorable outcomes are landing on blue or green, which are $2$ out of the $4$ sections. $\newline$ Probability = Number of favorable outcomes / Total number of outcomes $\newline$ Probability = $\frac{2}{4}$ $\newline$ Probability = $0.5$
Win Raffle: Calculate the probability of winning a raffle after buying $80$ out of $100$ tickets. $\newline$ There are $100$ tickets sold in total. If you buy $80$ tickets, you have $80$ chances to win. $\newline$ Probability = Number of favorable outcomes / Total number of outcomes $\newline$ Probability = $\frac{80}{100}$ $\newline$ Probability = $0.8$
Pull Chew: Calculate the probability of reaching into a bag and pulling out a strawberry chew. $\newline$ There are $60$ chews in total ( $3$ strawberry + $57$ cherry). The favorable outcome is pulling out one of the $3$ strawberry chews. $\newline$ Probability = Number of favorable outcomes / Total number of outcomes $\newline$ Probability = $\frac{3}{60}$ $\newline$ Probability = $0.05$
Compare Probabilities: Compare the probabilities to determine which event is most likely to occur. $\newline$ The probabilities calculated are: $\newline$ - Rolling a number greater than or equal to $3$ on an eight-sided die: $0.75$ $\newline$ - Spinning a spinner and landing on blue or green: $0.5$ $\newline$ - Winning a raffle after buying $80$ out of $100$ tickets: $0.8$ $\newline$ - Pulling out a strawberry chew: $0.05$ $\newline$ The event with the highest probability is winning the raffle after buying $80$ out of $100$ tickets, with a probability of $0.8$ .