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Vika [28.1K]
3 years ago
8

Roll a number cube. If the number cube comes up odd, you win the same number of points as the number on the cube. If the number

comes up even, you lose 4 points. What is the expected number of points per roll?
–0.25

–0.5

0

0.25

0.5
Mathematics
2 answers:
S_A_V [24]3 years ago
8 0

Answer:

-0.5

Step-by-step explanation:

laila [671]3 years ago
5 0

Answer:

–0.5

Step-by-step explanation:

Expected value is found by multiplying the probabilities of each roll by the amount won or lost with each roll.

The odd rolls are 1, 3 and 5.  The probability of rolling a 1 is 1/6, and the value is 1; this gives us 1/6(1) = 1/6.

The probability of rolling a 3 is 1/6, and the value is 3; this gives us 1/6(3) = 3/6.

The probability of rolling a 5 is 1/6, and the value is 5; this gives us 1/6(5) = 5/6.

Rolling any even number gives us the same value.  The probability of rolling an odd number is 3/6, and the value is -4; this gives us 3/6(-4) = -12/6.

Together we have

1/6+3/6+5/6-12/6 = 4/6+5/6-12/6 = 9/6-12/6 = -3/6 = -0.5

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Answer:

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Step-by-step explanation:

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Prove Forall x elementof Z, x^2 - 5x - 1 is odd.
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Answer with Step-by-step explanation:

Let Z be a set of integers

We have to prove that x^2-5x-1 is odd for all value of x \inZ.

There are two cases

1.When x is an odd integer number

2.when x is even integer number

1.When x is an odd integer  number

When x is positive odd integer

Then x^2  is positive odd number (because square of odd positive number is always positive an odd number )

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Hence ,x^2-5x-1 is an odd number .

When x is negative odd number

Then  x square is positive odd number  and 5x is negative odd term term

Therefore,odd number + odd number -1=Even  number -1=Odd number

Hence x^2-5x-1 is an odd number.

2.When  x is an even number

When x is positive even number

x square is positive even number  and 5x is positive even number

Even number -Even number -1 =Even number -odd number =Odd number

Suppose x=4

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When x is negative even number

Then x square is positive even number  and 5x is negative even number

x^2-5x-1=Even number +Even number -1=Even number -1=Odd number

Hence, for all elements of Zx^2-5x-1is odd.

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