Question

Suppose the dial on the spinner is spun 2 times in a row.

X is the number of times the dial lands on region A or B.

Which table represents the probability distribution for the variable X?

X P
0 1919
1 4949
2 4949

X P
0 2323
1 1313
2 1313

X P
0 827827
1 2323
2 127127

X P
0 1313
1 1313
2 1313

Answer 1

I think the answer to this is c

Answer 2

Answer:

The Dial on the Spinner is Spun 2 times in a row.

X= Number of times the dial lands on region A or B.

Variable X can take values =0 , 1, 2

There are three regions.

0=Neither on region A nor on region B

1= Region A

2= Region B

Considering equal probabilities of three regions

→Probability (Neither on region A nor on region B)=Probability (Region A)=Probability(Region B)

    $=\frac{1}{3}$

When, x=0

Means 2 failure and 0 Success that is 2 times neither on region A nor on region B

Probability (X=0 success)

$\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}$

Probability (X=1 success), one time on region A or B, and one time neither on region A nor on region B

$\frac{2}{3}*\frac{1}{3}+\frac{1}{3}*\frac{2}{3}=\frac{4}{9}$

Probability (X=1 success), one time on region A or B, and one time neither on region A nor on region B

$\frac{2}{3}\times\frac{2}{3}=\frac{4}{9}$

Option A:

X                             P

0                  $=\frac{1}{9}$

1                      $=\frac{4}{9}$

2                      $=\frac{4}{9}$