In a class, 60% of the students are girls, and 70% of the students like math.…
2025
In a class, 60% of the students are girls, and 70% of the students like math. If 80% of the girls like math, what is the probability that a randomly selected math-loving student is a girl ?
- A.
0.68
- B.
0.25
- C.
0.50
- D.
0.42
Attempted by 13 students.
Show answer & explanation
Correct answer: A
Step-by-Step Solution
To find the probability that a student is a girl given that they like math, we use Bayes' Theorem.
Identify the given probabilities:
Probability that a student is a girl: P(Girl) = 0.60
Probability that a student likes math: P(Math) = 0.70
Probability that a girl likes math (conditional probability): P(Math | Girl) = 0.80
State Bayes' Theorem:
We want to find P(Girl | Math), which is the probability that the student is a girl given they like math.
The formula is: P(Girl | Math) = [P(Math | Girl) * P(Girl)] / P(Math)
Substitute the values:
P(Girl | Math) = (0.80 * 0.60) / 0.70
P(Girl | Math) = 0.48 / 0.70
P(Girl | Math) ≈ 0.6857
Rounding to two decimal places, we get 0.68.