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State true or false.

A game consists of spinning an arrow that comes to rest pointing at one of the regions $1, 2, o r 3$ .

The outcomes $1, 2, 3$ are equally likely to occur.

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True

False

answer is B.

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Detailed Solution

Given that, a spinning wheel.
Question Image

We know that, a circle forms

360 °

.
So,

n (S) = 360 °

.
From the diagram, the region 1 forms

90 °

n (A) = 90 °

Let

A

be the event of an arrow resting at the region 1, then the probability of the event can be calculated by,

P (A) = N u m b e r of favourable outcomes T o t a l number of outcomes

P (A) = 90 ° 360 ° = 14

From the diagram, the region 2 forms

90 °

n (B) = 90 °

Let

B

be the event of an arrow resting at the region 2, then the probability of the event can be calculated by,

P (B) = N u m b e r of favourable outcomes T o t a l number of outcomes

P (B) = 90 ° 360 ° = 14

From the diagram, the region 3 forms

180 °

n (C) = 180 °

Let

C

be the event of an arrow resting at the region 3, then the probability of the event can be calculated by,

P (A) = N u m b e r of favourable outcomes T o t a l number of outcomes

P (C) = 180 ° 360 ° = 12

The area of the region

1

and

2

is equal but different from the area of the region

3

.
So the probability for the region

3

is more likely to occur as compared to the area of regions

1

and

2

.
So the correct statement is the outcomes

1, 2, 3

are not equally likely to occur.
Hence, the statement is false.
Therefore, option 2 is correct.

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