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Viefleur [7K]
1 year ago
14

on a popular fictional game show, contestants are given the opportunity to win money by reaching into a bag after being blindfol

ded and selecting a chip with a dollar amount written on it. assume all chips are identical. the bag contains four chips with a $0 amount, six chips with $1, five chips with $5, two chips with $10, and one chip with $100. the chips are mixed in the bag before the contestant draws their chip. a. construct a probability mass function (pmf) for x, the dollar amount won by a contestant in this game. b. what is the expected value for x?
Mathematics
1 answer:
labwork [276]1 year ago
8 0

Construct a probability mass function (pmf) for x, the dollar amount won by a contestant in this game is 1/18.

What is a probability math example?

  • Probability is the measurement of how likely something is to happen.
  • As an example, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head.
  • We write P(heads) = 12 here. The four most popular approaches to probability are axiomatic, classical, empirical, and subjective.

from above total number of chips =4+6+5+2+1 =18

hence Probabilty of win 0 P(0)=4/18

P(1) =6/18

P(5) =5/18

P(10) =2/18

P(100)=1/18

x     P(x)     xP(x)

0    0.22     0.00

1     0.33      0.33

5     0.28       1.39

10      0.11       1.11

100     0.06      5.56

                       8.39

therefore expeted value =8.39

Learn more about probability

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Problem 1:

Multiply Equation 1 by 4, keep Equation 2 the same.

x+y=8, multiply each term by 4:

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so, the equivalent system is: 4x+4y=32 and x-y=2

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4(y+2)+4y=32---> 4y+8+4y=32--->8y=24---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 1 Answer:

Equivalent system: 4x+4y=32, x-y=2; solution: x=5, y=3

Problem 2:

Keep Equation 1 the same. Add 1 and 2.

To add an equation, add the left sides together, and then the rights.

so: x+y=8 + x-y=2 gives us: 2x=10

solve for x ---> 2x/2=10/2--->x=5

plug x into x+y=8--->5+y=8--->y=3

Problem 2 answer:

Equivalent system: x+y=8, 2x=10; solution:x=5, y=3

Problem 3:

Subtract Equation 2 from 1, and keep 2 the same.

To subtract an equation, subtract the left sides, then the rights. We are subtracting 1<em> from </em>2, so its 2-1.

x-y=2 - x+y=8 gives us: -2y=-6

Solve for y by dividing by -2-->-2y/-2=-6/-2---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 3 answer:

Equivalent system: -2y=-6, x-y=2; solution: x=5, y=3

Problem 4:

Multiply the sum of Equation 1 and 2 by a factor of 3. Keep equation 2 the same.

First we add 1 and 2: (we did this earlier) ---> 2x=10 ---> now we multiply it all by 3---> 2x*(3)=10*(3)---> this gives us: 6x=30---> now divide by 6 to solve for x: 6x/6=30/6 gives us: x=5

Now, solve for y by plugging x into equation 2: x-y=2---> 5-y=2--->y=3

Problem 4 answer:

Equivalent system: 6x=30, x-y=2; solution: x=5, y=3

______

Quick Tip: One thing inherent of Equivalent systems is that they have the same set of solutions. Thus, we know the systems are equivalent when they have the same set of solutions for x and y. Moreover, you don't need to solve every time after you attempt to find an equivalent system, instead, just plug in the values found in problem 1 to each new set of equations to test if they are equivalent.

If we find x=5 and y=3 for x+y=8 and x-y=2, then all we have to do is plug them in to 6x=30 and -2y=-6 to see if they are equivalent.

6(5)=30 ---> true

-2(3)=-6 ---> true

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