Which event is most likely to occur? $\newline$ Rolling a multiple of $3$ on a eight-sided die, numbered from $1$ to $8$ . $\newline$ Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on red or blue or purple. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $88$ tickets. $\newline$ Reaching into a bag full of $1$ strawberry chews and $39$ 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 multiple of

3

on a eight-sided die, numbered from

1

8

\newline

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

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

88

tickets.

\newline

Reaching into a bag full of

1

strawberry chews and

39

cherry chews without looking and pulling out a strawberry chew.

Event $1$ Analysis: Let's analyze each event to determine its probability. $\newline$ Event $1$ : Rolling a multiple of $3$ on an eight-sided die, numbered from $1$ to $8$ . $\newline$ Multiples of $3$ in this range are $3$ and $6$ . So there are $2$ favorable outcomes. $\newline$ The probability of rolling a multiple of $3$ is the number of favorable outcomes divided by the total number of outcomes. $\newline$ Probability = Number of favorable outcomes / Total number of outcomes $\newline$ Probability = $\frac{2}{8}$ $\newline$ Probability = $\frac{1}{4}$
Event $2$ Analysis: Event $2$ : Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on red or blue or purple. $\newline$ There are $3$ favorable outcomes (red, blue, purple). $\newline$ The probability of landing on red, blue, or purple is the number of favorable outcomes divided by the total number of outcomes. $\newline$ Probability = Number of favorable outcomes / Total number of outcomes $\newline$ Probability = $\frac{3}{5}$
Event $3$ Analysis: Event $3$ : Winning a raffle that sold a total of $100$ tickets, if you buy $88$ tickets. $\newline$ The probability of winning the raffle is the number of tickets you have divided by the total number of tickets sold. $\newline$ Probability = Number of your tickets / Total number of tickets $\newline$ Probability = $\frac{88}{100}$ $\newline$ Probability = $0.88$
Event $4$ Analysis: Event $4$ : Reaching into a bag full of $1$ strawberry chew and $39$ cherry chews without looking and pulling out a strawberry chew. $\newline$ There is $1$ favorable outcome (strawberry chew). $\newline$ The probability of pulling out a strawberry chew is the number of favorable outcomes divided by the total number of outcomes. $\newline$ Probability $=$ Number of favorable outcomes $/$ Total number of outcomes $\newline$ Probability $= \frac{1}{40}$
Comparison and Conclusion: Now, let's compare the probabilities of each event to determine which is most likely to occur. $\newline$ Event $1$ : Probability = $\frac{1}{4} = 0.25$ $\newline$ Event $2$ : Probability = $\frac{3}{5} = 0.60$ $\newline$ Event $3$ : Probability = $0.88$ $\newline$ Event $4$ : Probability = $\frac{1}{40} = 0.025$ $\newline$ The event with the highest probability is Event $3$ , winning a raffle with $88$ out of $100$ tickets.