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.

Which table represents the probability distribution for the variable X?

Answer 1

if this is your spinner the answer is

the answer is

X P

0 1/9

1 4/9

2 4/9

Answer 2

If you spin the dial two times there three things that can happen:
1) Dial does not land in the region A
2) Dial lands once in the region A
3) Dial lands twice in the region A
The combined probability of these three events has to be 1.
Let's calculate probabilities of each event:

`1) P=P(1,1)=(2)/(3)\cdot(2)/(3)=(4)/(9)\\ 2)P=P(1,2)+P(2,1)=2\cdot (2)/(3)\cdot (1)/(3)=(4)/(9)\\ 3)P=P(3,3)=(1)/(3)\cdot(1)/(3)=(1)/(9)`
If we summ all those probabilities we get 1.
The answer would table C (lower left corner).