ACT (Enhanced)MathematicsEasy
A quality control engineer is inspecting a batch of 50 circuit boards. If the probability of a single circuit board being defective is 0.05, what is the expected number of defective circuit boards in the batch?
- A3.0
- B1.5
- C5.0
- D2.5
Show answer & explanationAnswer & explanation
Correct answer: D. 2.5
The expected number of events in a series of trials is calculated by multiplying the number of trials by the probability of the event occurring in a single trial. Expected value = Number of trials * Probability = 50 * 0.05 = 2.5.
Why the other options are wrong
- A. Incorrect calculation, possibly 50 * 0.06 or similar error.
- B. Incorrect calculation, possibly 50 * 0.03 or similar error.
- C. Incorrect calculation, possibly 50 * 0.10 or misinterpretation of the decimal.
Expected Value (Probability)
The expected value of a discrete random variable is the sum of the products of each possible value of the variable and its probability. For a binomial experiment, it's n*p.
- Represents the average outcome if the experiment were repeated many times.
- Can be a non-integer even if outcomes are integers.
- Used in decision-making and risk assessment.
Memory trick: Probability is the 'chance' of things happening, like a roll of the dice.