Below are four versions of the same game. Your archnemesis gets to pick the version of the game, and then you get to choose how many times to flip a coin: 10 times or 100 times. Identify how many coin flips you should choose for each version of the game. It costs $1 to play each game. Explain your reasoning.

The question is incomplete! The complete question along with answer and explanation is provided below.

Question:

Four games, one winner. Below are four versions fo the same game. Your archenmisis gets to pick the version of the game, and then you get to choose how many times to flip a coin: 10 times or 100 times. Identify how many coin flips you should choose for each version of the game. It costs $1 to play each game. Explain your reasoning.

(a) If the proportion of heads is larger than 0.60, you win $1.

(b) If the proportion of heads is larger than 0.40, you win $1.

(c) If the proportion of heads is between 0.40 and 0,60, you win $1.

(d) If the proportion of heads is smaller than 0.30, you win

Provided below please also refer to the attached image for better understating.

Step-by-step explanation:

The law of large numbers: As the number of trials increases the result tends towards the expected probability.

For example in case of a coin flips, the expected result of getting a head is 0.50 so as we increase the number of flips the end results is more likely to be close to 0.50.

When we have less number of flips then there is more variability which means end result is more likely to be away from expected result.

a) Since we want to have a probability (P>0.60) that is away from the expected probability (P=0.50) then we should have less number of flips.

So n = 10 should be selected.

b) Since we want to have a probability (P>0.40) that is close or going towards the expected probability (P=0.50) then we should have more number of flips.

So n = 100 should be selected.

b) Since we want to have a probability (0.40 < P < 0.60) that is close to the expected probability (P=0.50) then we should have more number of flips.

So n = 100 should be selected.

d) Since we want to have a probability (P<0.30) that is away from the expected probability (P=0.50) then we should have less number of flips.

So n = 10 should be selected.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

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