Maths: Applications and Interpretation · Statistics and probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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A discrete random variable X takes separate values, such as 0, 1, 2, 3, each with its own probability. The table of values and probabilities is its probability distribution, and the probabilities must add up to 1.
The expected value E(X) is the long-run average of X over many trials. A game is fair when the expected gain of the player is zero, which means the expected winnings equal the cost of playing.
The binomial distribution B(n, p) counts the number of successes in n trials. It needs a fixed number of trials, two outcomes for each trial, the same probability p each time and independent trials. Use your calculator for the probabilities.
For "at least r" students use 1 − P(X ≤ r), which removes r as well. The correct form is P(X ≥ r) = 1 − P(X ≤ r − 1), for example P(X ≥ 4) = 1 − P(X ≤ 3).
Answer: Not fair: the player expects to lose $0.20 per game.
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