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ziro4ka [17]
3 years ago
12

Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, on

e chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). • Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) • What is Miguel’s expected value from playing the game? • Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? • What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation.
Mathematics
1 answer:
jolli1 [7]3 years ago
6 0

Answer:

See explanation

Step-by-step explanation:

<h3 /><h3>Step 1</h3>

Miguel wins $2 is if he pulls two chips with the number 1.  

<u>Probability of winning is: </u>

  • 2/4 * 1/3 = 1/6  as there are 4 chips in total

<u> Probability of loosing is:</u>

  • 1- 1/6 = 5/6
<h3 /><h3>Step 2</h3>

<u>Missing values we found in the step 1, can be populated in the table:</u>

  • Xi === 2 === -1
  • P(Xi) === 1/6 === 5/6

<u>Expected Value as per table data:</u>

  • 1/6*2 + 5/6*(-1) = -1/2

Expected value is $1/2 loss each time he plays

<h3 /><h3>Step 3</h3>

To make the game fair, the expected value should be zero.

<u>Then as per the calculation above, let's replace 2, with x, and find its value.</u>

  • 1/6x + 5/6*(-1) = 0      
  • 1/6x = 5/6                  
  • x= 5  

So the amount should be $5 to make the game fair.

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Answer:

The total change in water level over the past 2 years is \displaystyle -4 \frac{1}{6}.

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Fractions

  • Proper and Improper

Numbers

  • Least Common Multiple (LCM)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

Year 1 water change:  \displaystyle -2 \frac{1}{3}

Year 2 water change:  \displaystyle -1 \frac{5}{6}

<u>Step 2: Find Total Water Change</u>

  1. [Set up] Add yearly water changes:                                                                \displaystyle -2 \frac{1}{3} + -1 \frac{5}{6}
  2. [Fractions] Convert to improper:                                                                     \displaystyle \frac{-7}{3} - \frac{11}{6}
  3. [Fraction] Rewrite [LCM]:                                                                                  \displaystyle \frac{-14}{6} - \frac{11}{6}
  4. [Order of Operations] Subtract:                                                                       \displaystyle \frac{-25}{6}
  5. [Fraction] Convert to proper:                                                                           \displaystyle -4 \frac{1}{6}
5 0
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