Question

Of all the seniors at a local high school, 5% take both calculus and economics, 30% take neither calculus or economics, and 50% do not take calculus. What percentage of all the seniors take economics?

Answer 1

C = Event of taking Calculus.

E= Event of taking Economics.

5% take both calculus and economics, so, P(C E ) = 0.05

30% take neither calculus nor economics, so, 1- P(C E ) = 0.3 , or, P(C E ) = 0.7

50% do not take calculus, so, 1- P(C) = 0.5 , or , P(C) = 0.5

We know,

P(C E )= P(C) + P ( E) - P(C E )

or, 0.7 = 0.5 + P(E) - 0.05

or, P(E) = 0.25

Percentage of all the seniors, who take economics is 25 %

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