Math 3 Quiz: Expected Value
4 questions · exam conditions
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Expected ValueQuestion 1 of 4

A quality control inspector tests electronic components and finds that 80% pass inspection, 15% have minor defects (can be sold at 70% of full price), and 5% have major defects (must be scrapped, resulting in a total loss). If each component costs $20 to produce and sells for $50 when it passes inspection, what is the expected profit per component?

$22.05
$24.50
$26.75
$28.25
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Math 3 Quiz

Math 3 Quiz: Expected Value

Practice Expected Value in Math 3 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Expected Value, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 3.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A quality control inspector tests electronic components and finds that 80% pass inspection, 15% have minor defects (can be sold at 70% of full price), and 5% have major defects (must be scrapped, resulting in a total loss). If each component costs $20 to produce and sells for $50 when it passes inspection, what is the expected profit per component?

  1. $22.05 (correct answer)
  2. $24.50
  3. $26.75
  4. $28.25
Explanation: For each component, the cost is always $20. The revenue depends on the outcome: Pass (80%): revenue = $50, profit = $50 - $20 = $30. Minor defect (15%): revenue = $50 × 0.70 = $35, profit = $35 - $20 = $15. Major defect (5%): revenue = $0, profit = $0 - 20=−20 = -20. Expected profit = 0.80(30) + 0.15(15) + 0.05(-20) = 24 + 2.25 - 1 = $22.05.

Question 2

A basketball player's scoring follows this pattern: she scores 0 points with probability 0.3, 2 points with probability 0.4, 3 points with probability 0.2, and 4 points with probability 0.1. In a tournament format, her score for each game is doubled if her team wins (which happens 60% of the time), but remains the same if they lose. What is her expected score per game in this tournament?

  1. 2.642.64
  2. 3.123.12 (correct answer)
  3. 3.683.68
  4. 4.164.16
Explanation: First, find the expected score before considering wins/losses: E[basic score] = 0(0.3) + 2(0.4) + 3(0.2) + 4(0.1) = 0 + 0.8 + 0.6 + 0.4 = 1.8 points. In the tournament: if the team wins (probability 0.6), her score is doubled; if they lose (probability 0.4), her score stays the same. Expected tournament score = P(win) × 2 × E[basic score] + P(lose) × E[basic score] = 0.6 × 2 × 1.8 + 0.4 × 1.8 = 0.6 × 3.6 + 0.4 × 1.8 = 2.16 + 0.72 = 3.12 points.

Question 3

A taxi driver's daily income depends on the number of rides completed. On any given day, there's a 20% chance of completing 8 rides (240total),35240 total), 35% chance of 10 rides (300 total), 30% chance of 12 rides (360total),and15360 total), and 15% chance of 14 rides (420 total). If daily expenses (gas, maintenance, fees) average $85, what is the expected daily profit?

  1. $238 (correct answer)
  2. $245
  3. $252
  4. $259
Explanation: Expected daily income = 240(0.20) + 300(0.35) + 360(0.30) + 420(0.15) = 48 + 105 + 108 + 63 = $324. Expected daily profit = $324 - $85 = 239.TheclosestanswerisA(239. The closest answer is A (238). Choices B, C, and D represent common errors like forgetting to subtract expenses, miscalculating probabilities, or arithmetic mistakes in the expected value calculation.

Question 4

A game show has three doors, behind which are prizes worth $1000, $500, and $0. A contestant chooses a door randomly, then the host (who knows what's behind each door) opens one of the remaining doors that contains a prize worth less than $1000. The contestant can then switch to the other unopened door or keep their original choice. If the contestant always switches, what is the expected value of their prize?

  1. $500
  2. $600
  3. $666.67 (correct answer)
  4. $750
Explanation: This is a variant of the Monty Hall problem. Let's analyze each case based on the contestant's initial choice: Case 1: Initially chose $1000 door (probability 1/3). Host must open either the $500 or $0 door. If host opens $500 door, switching gives $0. If host opens $0 door, switching gives $500. Assuming host chooses randomly when both options are available, expected value from switching = (1/2)(0) + (1/2)(500) = $250. Case 2: Initially chose $500 door (probability 1/3). Host must open the $0 door (since host opens a door worth less than $1000). Switching gives $1000. Case 3: Initially chose $0 door (probability 1/3). Host must open the $500 door. Switching gives $1000. Expected value = (1/3)(250) + (1/3)(1000) + (1/3)(1000) = 250/3 + 1000/3 + 1000/3 = 2250/3 = $750. Wait, let me reconsider the host's strategy. The problem states the host opens a door with a prize worth less than $1000, so the host could open either the $500 or $0 door. Let me recalculate assuming the host always opens the door with the smallest available prize: Case 1: Initially chose $1000, host opens $0 door, switching gives $500. Case 2: Initially chose $500, host opens $0 door, switching gives $1000. Case 3: Initially chose $0, host opens $500 door, switching gives $1000. Expected value = (1/3)(500) + (1/3)(1000) + (1/3)(1000) = 2500/3 ≈ $666.67.