Educational Quiz Show Controversy?
A popular television quiz show has a 'lucky draw' segment where a contestant can win cash prizes by spinning a wheel. The wheel is divided into 10 equal sections - 5 in red and 5 in blue. If the wheel lands on any blue section, the contestant gets a 'free pass' to the next round, but if it lands on a red section, they must answer a difficult question correctly to proceed. What is the probability that a contestant will get at least one free pass in three spins of the wheel?
1 Answer
📌 CONCEPT: The probability of getting at least one free pass in three spins of the wheel can be found by calculating the probability of the complementary event (getting no free pass) and subtracting it from 1.
📐 RULE / FORMULA: To find the probability of getting at least one free pass, we can use the complementary probability formula: P(at least one free pass) = 1 - P(no free pass). The probability of getting no free pass in three spins is (5/10) × (5/10) × (5/10) since there are 5 red sections and 5 blue sections on the wheel.
💡 WORKED EXAMPLE: Suppose the probability of getting a free pass in one spin is 0.5. Then, the probability of getting no free pass in one spin is 1 - 0.5 = 0.5. Therefore, the probability of getting no free pass in three spins is 0.5 × 0.5 × 0.5 = 0.125.
⚠️ COMMON MISTAKE: Students often make the mistake of not considering the complementary probability or not calculating the probability of getting no free pass correctly.
01 Sept 26
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