In a group of 100 students, 60 students study Spanish and 40 students study French. Among … — GMAT

In a group of $100$ students, $60$ students study Spanish and $40$ students study French. Among the $60$ students studying Spanish, $15$ also study French. If a student who studies Spanish is selected at random, what is the probability that the selected student also studies French?

Cevap: 0.25

Cevap

The probability that a randomly selected Spanish-studying student also studies French is 0.25.

Since the student is chosen from the group of

60

Spanish-studying students, the sample space is restricted to

60

. Within this subset,

15

students study French. The conditional probability is therefore

\frac{15}{60} = 0.25

Adım Adım Çözüm

Identify the total number of outcomes in the restricted sample space.

The sample space is restricted to students studying Spanish:

n(\text{Spanish}) = 60

The question specifies that the student is chosen from those who study Spanish.

Identify the number of favorable outcomes within this restricted sample space.

The number of students studying both Spanish and French is

n(\text{Spanish} \cap \text{French}) = 15

We need the count of students who satisfy both the given condition and the target event.

Calculate the conditional probability.

P(\text{French} | \text{Spanish}) = \frac{15}{60} = 0.25

Conditional probability is calculated by dividing the intersection count by the given condition's total count.

Anahtar Kavram

Conditional Probability:

P(A|B) = \frac{n(A \cap B)}{n(B)}

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