At a county fair there is a spinner game with 12 sectors: 2 red sectors, 2 green sectors, 2 blue sectors, and 6 yellow sectors. if the spinner lands on a red sector, the player wins 2 tokens. if the spinner lands on a green sector, the player wins 2 tokens. if the spinner lands on a blue sector, the player wins 2 tokens. if the spinner lands on a yellow sector, the player loses 3 tokens. is this game fair for the player and how much will the player win or lose on an average over time? a) county fair games are never fair. b) the expected value is zero, and the game is fair. so the player will break even for a single spin over time. c) the expected values is 1 2 , and the game is fair. the player will win about 0.55 tokens on a single spin over time. d) the expected value is -0.5, and the game is not fair. so the player will lose about 0.5 tokens for a single spin over time.

Option D- The expected value is -0.5, and the game is not fair. So the player will lose about 0.5 tokens for a single spin over time.

Step-by-step explanation:

Given : At a County fair there is a spinner game with 12 sectors:  2 red sectors, 2 green sectors, 2 blue sectors, and 6 yellow sectors.

If the spinner lands on :

A red sector- the player wins 2 tokens.

A green sector- the player wins 2 tokens.

A blue sector- the player wins 2 tokens.

A yellow sector- the player loses 3 tokens.              

To find : Is this game fair for the player and how much will the player win or lose on an average over time?

Solution :

First we find the probability of each sector,

Total outcome = 12

1)

2)      

3)  

4)  

Now, For a win the profit is w=2 tokens.

For a loss, the profit is l= -3 tokens.      

Now, The expected value is the product of probability and its profit/loss.

Therefore, The game is not fair. So the player will lose about 0.5 tokens for a single spin over time.

Hence, Option D is correct.

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.