Which event is least likely to occur? $\newline$ Rolling an even number 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 blue or red. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $74$ tickets. $\newline$ Reaching into a bag full of $2$ strawberry chews and $18$ cherry chews without looking and pulling out a strawberry chew.

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Math Problems

Grade 7

Make predictions using experimental probability

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Q. Which event is least likely to occur?

\newline

Rolling an even number 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 blue or red.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

74

tickets.

\newline

Reaching into a bag full of

2

strawberry chews and

18

cherry chews without looking and pulling out a strawberry chew.

Event $1$ Probability: Let's evaluate the probability of each event happening. $\newline$ Event $1$ : Rolling an even number on a twelve-sided die, numbered from $1$ to $12$ . $\newline$ There are $6$ even numbers on a twelve-sided die ( $2$ , $4$ , $6$ , $8$ , $10$ , $12$ ). $\newline$ Probability of rolling an even number = Number of even numbers / Total numbers on the die $\newline$ = $6 / 12$ $\newline$ = $12$ $0$
Event $2$ Probability: Event $2$ : Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on blue or red. $\newline$ There are $2$ favorable outcomes (blue or red) out of $5$ possible outcomes. $\newline$ Probability of landing on blue or red = Number of favorable outcomes / Total number of outcomes $\newline$ = $\frac{2}{5}$
Event $3$ Probability: Event $3$ : Winning a raffle that sold a total of $100$ tickets, if you buy $74$ tickets. $\newline$ Probability of winning the raffle $=$ Number of tickets you buy $/$ Total number of tickets sold $\newline$ $=$ $\frac{74}{100}$ $\newline$ $= 0.74$
Event $4$ Probability: Event $4$ : Reaching into a bag full of $2$ strawberry chews and $18$ cherry chews without looking and pulling out a strawberry chew. $\newline$ Probability of pulling out a strawberry chew $= \frac{\text{Number of strawberry chews}}{\text{Total number of chews}}$ $\newline$ $= \frac{2}{2 + 18}$ $\newline$ $= \frac{2}{20}$ $\newline$ $= \frac{1}{10}$
Comparison of Probabilities: Now, let's compare the probabilities to determine which event is least likely to occur. $\newline$ Event $1$ : $\frac{1}{2} = 0.5$ $\newline$ Event $2$ : $\frac{2}{5} = 0.4$ $\newline$ Event $3$ : $0.74$ $\newline$ Event $4$ : $\frac{1}{10} = 0.1$ $\newline$ The event with the smallest probability is the least likely to occur.
Least Likely Event: The event with the smallest probability is Event $4$ , with a probability of $0.1$ or $\frac{1}{10}$ . Therefore, reaching into a bag full of $2$ strawberry chews and $18$ cherry chews without looking and pulling out a strawberry chew is the least likely to occur.