NationalMediumProbability10–12

Conditional Probability from a Two-Way Count

Probabilidade Condicionada a Partir de uma Contagem Cruzada

In a school with $200$ students, $120$ study Spanish and $80$ do not. Of those who study Spanish, $45$ also play in the school band; of those who do not study Spanish, $20$ play in the band. A student is chosen at random and plays in the band. What is the probability that this student studies Spanish?

Only the students who play in the band are still in the running: the extra information shrinks the sample space before the question is even asked. Decide what that new whole is before writing any fraction.

Solution

Step 1 of 4

1.Students in the band: $45 + 20 = 65$