Which event is least likely to occur? $\newline$ Rolling a $2$ on a six-sided die, numbered from $1$ to $6$ . $\newline$ Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on red or blue. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $42$ tickets. $\newline$ Reaching into a bag full of $66$ strawberry chews and $14$ 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 least likely to occur?

\newline

Rolling a

2

on a six-sided die, numbered from

1

6

\newline

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

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

42

tickets.

\newline

Reaching into a bag full of

66

strawberry chews and

14

cherry chews without looking and pulling out a strawberry chew.

Evaluate Probability: First, let's evaluate the probability of each event happening.
Event $1$ : Event $1$ : Rolling a $2$ on a six-sided die. $\newline$ The probability of rolling a $2$ is $1$ out of $6$ , since there is only one side with a $2$ and six possible outcomes. $\newline$ Probability = $\frac{1}{6}$
Event $2$ : Event $2$ : Spinning a spinner divided into four equal-sized sections and landing on red or blue. $\newline$ There are two favorable outcomes (red or blue) out of four possible outcomes. $\newline$ Probability = $\frac{2}{4} = \frac{1}{2}$
Event $3$ : Event $3$ : Winning a raffle that sold a total of $100$ tickets, if you buy $42$ tickets. $\newline$ The probability of winning is the number of tickets you have over the total number of tickets. $\newline$ Probability = $\frac{42}{100}$
Event $4$ : Event $4$ : Reaching into a bag with $66$ strawberry chews and $14$ cherry chews and pulling out a strawberry chew. $\newline$ The probability of pulling out a strawberry chew is the number of strawberry chews over the total number of chews. $\newline$ Probability = $\frac{66}{66+14} = \frac{66}{80} = \frac{33}{40}$
Compare Probabilities: Now, let's compare the probabilities to determine which event is least likely to occur. $\newline$ $\frac{1}{6}$ (Event $1$ ) is approximately $0.1667$ $\newline$ $\frac{1}{2}$ (Event $2$ ) is $0.5$ $\newline$ $\frac{42}{100}$ (Event $3$ ) is $0.42$ $\newline$ $\frac{33}{40}$ (Event $4$ ) is $0.825$
Least Likely Event: The event with the smallest probability is the one that is least likely to occur. $\newline$ Comparing the probabilities: $0.1667$ (Event $1$ ) $<$ $0.42$ (Event $3$ ) $<$ $0.5$ (Event $2$ ) $<$ $0.825$ (Event $4$ )
Least Likely Event: The event with the smallest probability is the one that is least likely to occur. Comparing the probabilities: $0.1667$ (Event $1$ ) $<$ $0.42$ (Event $3$ ) $<$ $0.5$ (Event $2$ ) $<$ $0.825$ (Event $4$ ) Therefore, the event that is least likely to occur is rolling a $2$ on a six-sided die.