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Maths · Probability scale

Crossover

In a survey, every person chose exactly one favourite from four films A, B, C and D. For a person chosen at random from the survey, P(A)=38P(A) = \frac{3}{8}, P(B)=P(C)P(B) = P(C), and P(D)P(D) is half of P(B)P(B). Fewer than 100 people took part, and the number of people who chose D is a prime number. How many different values are possible for the number of people surveyed?

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