Question

Given the spinner below that is divided evenly into 4 sections. Given that you spin the spinner two times. Let event F be the event in which you spin the spinner twice and get the same color. Let event H be the event that you spin the spinner twice and you get at least one green.Create a Venn diagram that shows the relationship between F, H, and the sample space.

Describe the events of F' and list the outcomes of this event.

Answer 1

Answer and Step-by-step explanation:

Read it Well before you answer

To describe the event F', we need to understand what the complement of event F represents. The complement of event F, denoted as F', refers to all the outcomes that are not in event F.

In this case, event F represents spinning the spinner twice and getting the same color. Therefore, event F' would represent spinning the spinner twice and not getting the same color.

Now, let's list the outcomes of event F':

- Blue-Green: This outcome occurs when the spinner lands on blue in the first spin and green in the second spin.

- Green-Blue: This outcome occurs when the spinner lands on green in the first spin and blue in the second spin.

- Green-Red: This outcome occurs when the spinner lands on green in the first spin and red in the second spin.

- Red-Green: This outcome occurs when the spinner lands on red in the first spin and green in the second spin.

- Blue-Red: This outcome occurs when the spinner lands on blue in the first spin and red in the second spin.

- Red-Blue: This outcome occurs when the spinner lands on red in the first spin and blue in the second spin.

These outcomes represent all the possible combinations where the spinner does not land on the same color in both spins, which is the complement of event F.

To summarize, event F' represents spinning the spinner twice and not getting the same color. The outcomes of event F' are: Blue-Green, Green-Blue, Green-Red, Red-Green, Blue-Red, and Red-Blue.

Answer 2

See the attachment for the Venn diagram.

Explanation:

The sample space diagram for spinning the spinner twice is:

`\phantom{wwwwwwwwwwwwwww}\textsf{Second spin}\\\\\textsf{First spin}\;\;\begin{array}cccc\cline{1-5}&\sf Red&\sf Blue & \sf Green&\sf Yellow\\ \cline{1-5}\sf Red & RR&RB&RG&RY\\\sf Blue &BR&BB&BG&BY\\\sf Green&GR&GB&GG&GY\\ \sf Yellow &YR&YB&YG&YY\\\cline{1-5}\end{array}`

The total number of outcomes is 16.

Given event F is the event in which you spin the spinner twice and get the same color, then the outcomes of event F are:

• RR, BB, YY, GG.

Given event H is the event that you spin the spinner twice and get at least one green, then the outcomes of event H are:

• GR, GB, GG, GY, RG, BG, YG

There is one outcome that is common to both events:

• GG

To draw a Venn diagram that shows the relationships between F, H and the sample space:

• Draw two overlapping circles and label them F and H.
• Place GG in the overlapping region, since this outcome is common to both events.
• Place RR, BB and YY in the part of circle F to the left of the overlapping region.
• Place GR, GB, GY, RG, BG, YG in the part of circle H to the right of the overlapping region.
• Place RB, RY, BR, BY, YR, YB outside the circles.

The event F' represents the complement of event F, which consists of all outcomes that are not in event F. Therefore, if event F is the event in which you spin the spinner twice and get the same color, then event F' is the event in which you spin the spinner twice and do not get the same color.

The 12 outcomes of event F' are:

• RG (spinning red and green)
• RB (spinning red and blue)
• RY (spinning red and yellow)
• GR (spinning green and red)
• GB (spinning green and blue)
• GY (spinning green and yellow)
• BR (spinning blue and red)
• BG (spinning blue and green)
• BY (spinning blue and yellow)
• YR (spinning yellow and red)
• YG (spinning yellow and green)
• YB (spinning yellow and blue)