Question

There are two spinners containing only white and green slices.

Spinner A has 10 green slices and 6 white slices.
All the slices are the same size.
Spinner B has 11 green slices and 9 white slices.
All the slices are the same size.
Each spinner is spun.
List these events from least likely to most likely.
Event 1: Spinner B lands on a green slice.
Event 2: Spinner A lands on a purple slice.
Event 3: Spinner A lands on a green slice.
Event 4: Spinner B lands on a green or white slice.
Least likely
Most likely
Event Event Event Event

Answer 1

`\textsf{Least likely --------------------------$ > $ Most likely}\\\\\textsf{Event $\boxed{2}$\;,\;\;Event $\boxed{1}$\;,\;\;Event $\boxed{3}$\;,\;\;Event $\boxed{4}$}`

Explanation:

To determine the likelihood of each event, calculate the probability of each event happening.

`\boxed{\sf Probability\:of\:an\:event\:occurring = (Number\:of\;favorable\;outcomes)/(Total\:number\:of\:possible\:outcomes)}`

Favorable outcomes are the number of outcomes or events that meet a specific condition.

Given the information provided, calculate the probabilities for each event.

`\hrulefill`

Event 1: Spinner B lands on a green slice

Number of favorable outcomes = 11 (green)

Total number of favorable outcomes = 11 (green) + 9 (white) = 20

`\textsf{P(Spinner B: Green)}= (11)/(20)=0.55`

`\hrulefill`

Event 2: Spinner A lands on a purple slice

Spinner A does not have any purple slices. Therefore:

Number of favorable outcomes = 0

Total number of favorable outcomes = 10 (green) + 6 (white) = 16

`\textsf{P(Spinner A: Purple)}=(0)/(16)=0`

`\hrulefill`

Event 3: Spinner A lands on a green slice

Number of favorable outcomes = 10 (green)

Total number of favorable outcomes = 10 (green) + 6 (white) = 16

`\textsf{P(Spinner A: Green)}= (10)/(16)=0.625`

`\hrulefill`

Event 4: Spinner B lands on a green or white slice

Total number of favorable outcomes = 10 (green) + 6 (white) = 16

`\textsf{P(Spinner B: Green)\;or\;P(Spinner B: White)}= (10)/(16)+(6)/(16)=1`

`\hrulefill`

The least likely event is the event with the smallest probability.

The most likely event is the event with the greatest probability.

Therefore, the events from least likely to most likely are:

`\textsf{Least likely --------------------------$ > $ Most likely}\\\\\textsf{Event $\boxed{2}$\;,\;\;Event $\boxed{1}$\;,\;\;Event $\boxed{3}$\;,\;\;Event $\boxed{4}$}`