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Which event is least likely to occur?
Rolling an even number on a twelve-sided die, numbered from 1 to 12.
Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on purple.
Winning a raffle that sold a total of 100 tickets, if you buy 74 tickets.
Reaching into a bag full of 6 strawberry chews and 14 cherry chews without looking and pulling out a strawberry chew.

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 purple. $\newline$ Winning a raffle that sold a total of $100$ tickets, if you buy $74$ tickets. $\newline$ Reaching into a bag full of $6$ strawberry chews and $14$ cherry chews without looking and pulling out a strawberry chew.

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Make predictions using experimental probability

Full solution

Q. 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 purple.

\newline

Winning a raffle that sold a total of

100

tickets, if you buy

74

tickets.

\newline

Reaching into a bag full of

6

strawberry chews and

14

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 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 number of sides $\newline$ = $\frac{6}{12}$ $\newline$ = $\frac{1}{2}$
Event $2$ Analysis: Event $2$ : Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on purple. $\newline$ Probability of landing on purple $=$ Number of purple sections / Total number of sections $\newline$ $= \frac{1}{5}$
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 $6$ strawberry chews and $14$ cherry chews without looking and pulling out a strawberry chew. $\newline$ Probability of pulling out a strawberry chew $= \frac{\text{Number of strawberry chews}}{\text{Total number of chews}}$ $\newline$ $= \frac{6}{(6 + 14)}$ $\newline$ $= \frac{6}{20}$ $\newline$ $= \frac{3}{10}$ $\newline$ $= \(0\).\(3\)
Comparison of Probabilities: Now, let's compare the probabilities to determine which event is least likely to occur.\(\newline\)Event \(1\): Probability = \(\frac{1}{2} = 0.5\)\(\newline\)Event \(2\): Probability = \(\frac{1}{5} = 0.2\)\(\newline\)Event \(3\): Probability = \(0.74\)\(\newline\)Event \(4\): Probability = \(0.3\)\(\newline\)The event with the smallest probability is the least likely to occur.
Least Likely Event: The event with the smallest probability is Event \(2\), spinning the spinner and landing on purple, with a probability of \(0.2\) or \(\frac{1}{5}\).

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