Question

In a game using a spinner with five equal parts numbered 1 to 5, a contestant wins when the spinner lands on an odd number. Is this game fair?A.yesB.noC.not enough information

Answer 1

A game is said to be fair if the probability of winning is equal to the probability of losing.

The sample space S is given by:

`S=\left\lbrace1,2,3,4,5\right\rbrace`

The event, W, that the spinner lands on an odd number is given by:

`W=\left\lbrace1,3,5\right\rbrace`

The event, L, that the spinner does not land on an odd number is given by:

`L=\left\lbrace2,4\right\rbrace`

The probability of an event E is given by:

`P\left(E\right)=(n\left(E\right))/(n\left(S\right))`

Therefore, the probability of W is given by:

`P\left(W\right)=(n\left(W\right))/(n\left(S\right))=(3)/(5)=0.6`

and

the probability of L is given by:

`P\left(L\right)=(n\left(L\right))/(n\left(S\right))=(2)/(5)=0.4`

Therefore,

`P\left(W\right)P\left(L\right)`

The probability of winning is not equal to the probability of losing.

Therefore, the game is not fair.

The correct answer is choice A

.