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 yellow or red. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $83$ tickets. $\newline$ Reaching into a bag full of $36$ 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 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 yellow or red.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

83

tickets.

\newline

Reaching into a bag full of

36

strawberry chews and

44

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 $3$ on an eight-sided die. $\newline$ There are $8$ possible outcomes when rolling the die, and $6$ of these outcomes ( $3, 4, 5, 6, 7, 8$ ) are greater than or equal to $3$ . $\newline$ Probability = Number of favorable outcomes / Total number of possible outcomes $\newline$ Probability = $\frac{6}{8}$ $\newline$ Probability = $0.75$
Calculate Probability of Spinning: Calculate the probability of spinning the spinner and landing on yellow or red. $\newline$ There are $4$ equal sections, so there are $4$ possible outcomes. $2$ of these outcomes (yellow, red) are favorable. $\newline$ Probability $=$ Number of favorable outcomes $/$ Total number of possible outcomes $\newline$ Probability $= \frac{2}{4}$ $\newline$ Probability $= 0.5$
Calculate Probability of Winning: Calculate the probability of winning a raffle after buying $83$ out of $100$ tickets. $\newline$ There are $100$ possible outcomes, and buying $83$ tickets means $83$ favorable outcomes. $\newline$ Probability = Number of favorable outcomes / Total number of possible outcomes $\newline$ Probability = $\frac{83}{100}$ $\newline$ Probability = $0.83$
Calculate Probability of Pulling: Calculate the probability of reaching into a bag and pulling out a strawberry chew. There are $36$ strawberry chews and $44$ cherry chews, making a total of $80$ chews. Probability $= \frac{\text{Number of strawberry chews}}{\text{Total number of chews}}$ Probability $= \frac{36}{80}$ Probability $= $0$.$45$
Compare Probabilities: Compare the probabilities to determine which event is most likely to occur.$\newline$The probabilities calculated are:$\newline$Rolling a number $\geq 3$ on an eight-sided die: $0.75$$\newline$Spinning and landing on yellow or red: $0.5$$\newline$Winning the raffle with $83$ tickets: $0.83$$\newline$Pulling out a strawberry chew: $0.45$$\newline$The highest probability is associated with winning the raffle with $83$ tickets.