State true or false.A game consists of spinning an arrow that comes to rest pointing at one of the regions

1, 2, or 3

. The outcomes

1,2,3
are equally likely to occur.

Question

State true or false.A game consists of spinning an arrow that comes to rest pointing at one of the regions

1, 2, or 3
   
 . The outcomes

1,2,3
  are equally likely to occur.

Accepted Answer

Given that, a spinning wheel.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)=
    
     Number of favourable outcomes
    
     Total number of outcomes

P(A)=
      
       90°
      
       360°

=
      1
      4

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)=
    
     Number of favourable outcomes
    
     Total number of outcomes

P(B)=
      
       90°
      
       360°

=
      1
      4

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)=
    
     Number of favourable outcomes
    
     Total number of outcomes

P(C)=
      
       180°
      
       360°

=
      1
      2

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.

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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State true or false.A game consists of spinning an arrow that comes to rest pointing at one of the regions 1, 2, or 3 . The outcomes 1,2,3 are equally likely to occur.