Which event is most likely to occur? $\newline$ Rolling a multiple of $3$ on a six-sided die, numbered from $1$ to $6$ . $\newline$ Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on red or blue or green. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $91$ tickets. $\newline$ Reaching into a bag full of $7$ strawberry chews and $33$ 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 six-sided die, numbered from

1

6

\newline

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

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

91

tickets.

\newline

Reaching into a bag full of

7

strawberry chews and

33

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 a six-sided die, numbered from $1$ to $6$ . $\newline$ The multiples of $3$ in this range are $3$ and $6$ . So there are $2$ favorable outcomes out of $6$ possible outcomes. $\newline$ Probability of rolling a multiple of $3$ = Number of favorable outcomes / Total number of outcomes = $\frac{2}{6} = \frac{1}{3}$ .
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 green. $\newline$ There are $3$ favorable outcomes (red, blue, green) out of $5$ possible outcomes. $\newline$ Probability of landing on red, blue, or green = Number of favorable outcomes / Total number of outcomes = $\frac{3}{5}$ .
Event $3$ Analysis: Event $3$ : Winning a raffle that sold a total of $100$ tickets, if you buy $91$ tickets. $\newline$ The probability of winning is the number of tickets you have over the total number of tickets. $\newline$ Probability of winning the raffle = Number of tickets you have / Total number of tickets = $\frac{91}{100}$ .
Event $4$ Analysis: Event $4$ : Reaching into a bag full of $7$ strawberry chews and $33$ cherry chews without looking and pulling out a strawberry chew. $\newline$ There are $7$ favorable outcomes (strawberry chews) out of $40$ total chews ( $7$ strawberry + $33$ cherry). $\newline$ Probability of pulling out a strawberry chew = Number of favorable outcomes / Total number of outcomes = $\frac{7}{40}$ .
Comparison of Probabilities: Now, let's compare the probabilities of each event to determine which is most likely to occur. $\newline$ Event $1$ : Probability = $\frac{1}{3} \approx 0.333...$ $\newline$ Event $2$ : Probability = $\frac{3}{5} = 0.6$ $\newline$ Event $3$ : Probability = $\frac{91}{100} = 0.91$ $\newline$ Event $4$ : Probability = $\frac{7}{40} = 0.175$ $\newline$ The event with the highest probability is Event $3$ , with a probability of $0.91$ .