In a board game, you roll a die to win or lose points, depending on the outcome. the outcomes follow this probability distribution.
if a player can only win by accumulating 20 points, which of the following best describes the fairness of the game?

Answer with explanation:

→Total faces on the dice and marked numbers =6={1,2,3,4,5,6}

If you are rolling the dice and getting number 1 and 5 , you win 4 and 6 points respectively.

And, If you roll the dice and getting number 2,3,4 and 6 , you loose -5  points .

→→So,suppose the dice is rolled 6 times, and considering each outcome to be equally likely

         then you loose more points than gaining which is equal to

   = 4+(-5)+(-5)+(-5)+6+(-5)

   =10-20

   = -10

And, Average

So, if number of outcomes are equally likely, you can't accumulate 20 points.

Option B:→ It is not a fair game because weighted average is Negative.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

the correct answers i think are b. and d.

give me brainliest if it is correct!