Which event is most likely to occur? $\newline$ Rolling a prime 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 red or yellow or green or purple. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $74$ tickets. $\newline$ Reaching into a bag full of $34$ strawberry chews and $46$ cherry chews without looking and pulling out a strawberry chew.

View step-by-step help

Home

Math Problems

Grade 7

Make predictions using experimental probability

Full solution

Q. Which event is most likely to occur?

\newline

Rolling a prime 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 red or yellow or green or purple.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

74

tickets.

\newline

Reaching into a bag full of

34

strawberry chews and

46

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 prime number on a twelve-sided die, numbered from $1$ to $12$ . $\newline$ Prime numbers between $1$ and $12$ are $2, 3, 5, 7, 11$ . There are $5$ prime numbers. $\newline$ Probability of rolling a prime number = Number of prime numbers / Total numbers on the die $\newline$ = $\frac{5}{12}$
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 yellow or green or purple. $\newline$ Since there are five equal sections and only one color we do not want to land on (blue), we have four favorable outcomes. $\newline$ Probability of landing on red, yellow, green, or purple = \frac{\text{Number of favorable colors}}{\text{Total number of colors}}$\newline= \frac{4}{5}$
Event $3$ Analysis: Event $3$ : Winning a raffle that sold a total of $100$ tickets, if you buy $74$ tickets. $\newline$ Probability of winning the raffle $= \frac{\text{Number of tickets you buy}}{\text{Total number of tickets sold}}$ $\newline$ $= \frac{74}{100}$ $\newline$ $= 0.74$
Event $4$ Analysis: Event $4$ : Reaching into a bag full of $34$ strawberry chews and $46$ cherry chews without looking and pulling out a strawberry chew. $\newline$ Total number of chews = $34$ (strawberry) + $46$ (cherry) $\newline$ = $80$ $\newline$ Probability of pulling out a strawberry chew = Number of strawberry chews / Total number of chews $\newline$ = $34 / 80$ $\newline$ = $0.425$
Comparison: Now, let's compare the probabilities to determine which event is most likely to occur. $\newline$ Event $1$ : Probability = $\frac{5}{12} \approx 0.4167$ $\newline$ Event $2$ : Probability = $\frac{4}{5} = 0.8$ $\newline$ Event $3$ : Probability = $0.74$ $\newline$ Event $4$ : Probability = $0.425$ $\newline$ The event with the highest probability is Event $2$ , spinning the spinner and landing on red, yellow, green, or purple.