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 red or blue or yellow or green. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $40$ tickets. $\newline$ Reaching into a bag full of $16$ strawberry chews and $44$ 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

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 red or blue or yellow or green.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

40

tickets.

\newline

Reaching into a bag full of

16

strawberry chews and

44

cherry chews without looking and pulling out a strawberry chew.

Event $1$ Analysis: Let's analyze each event to determine its probability of occurring. $\newline$ Event $1$ : Rolling a number greater than $4$ on a twelve-sided die, numbered from $1$ to $12$ . $\newline$ The numbers greater than $4$ on a twelve-sided die are $5, 6, 7, 8, 9, 10, 11,$ and $12$ . There are $8$ possible outcomes that satisfy the condition out of $12$ possible outcomes in total. $\newline$ Probability of Event $1$ = Number of favorable outcomes / Total number of outcomes = $\frac{8}{12} = \frac{2}{3}$
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 yellow or green. $\newline$ There are $4$ favorable outcomes (red, blue, yellow, green) out of $5$ possible outcomes. $\newline$ Probability of Event $2$ = Number of favorable outcomes / Total number of outcomes = $\frac{4}{5}$
Event $3$ Analysis: Event $3$ : Winning a raffle that sold a total of $100$ tickets, if you buy $40$ 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 of Event $3$ = Number of your tickets / Total number of tickets = $\frac{40}{100}$ = $\frac{2}{5}$
Event $4$ Analysis: Event $4$ : Reaching into a bag full of $16$ strawberry chews and $44$ cherry chews without looking and pulling out a strawberry chew. $\newline$ The total number of chews is $16$ (strawberry) + $44$ (cherry) = $60$ . $\newline$ The probability of pulling out a strawberry chew is the number of strawberry chews divided by the total number of chews. $\newline$ Probability of Event $4$ = Number of strawberry chews / Total number of chews = $\frac{16}{60}$ = $\frac{4}{15}$
Comparison and Conclusion: Now, let's compare the probabilities to determine which event is most likely to occur. $\newline$ Probability of Event $1$ = $\frac{2}{3} \approx 0.6667$ $\newline$ Probability of Event $2$ = $\frac{4}{5} = 0.8$ $\newline$ Probability of Event $3$ = $\frac{2}{5} = 0.4$ $\newline$ Probability of Event $4$ = $\frac{4}{15} \approx 0.2667$ $\newline$ The event with the highest probability is Event $2$ , spinning a spinner and landing on red, blue, yellow, or green.