In a group of 100 students, 60 play cricket, 50 play football, and 30 play…
2025
In a group of 100 students, 60 play cricket, 50 play football, and 30 play both. If a student is selected at random, what is the probability that the student plays cricket given that the student plays football ?
- A.
0.15
- B.
0.30
- C.
0.60
- D.
0.18
Attempted by 15 students.
Show answer & explanation
Correct answer: C
Step-by-Step Solution
To find the probability that a student plays cricket given that they play football, we use the formula for conditional probability: P(Cricket | Football) = P(Cricket ∩ Football) / P(Football).
Identify the total number of students: The total number of students is 100.
Determine the probability of playing football: We are given that 50 students play football, so P(Football) = 50 / 100 = 0.50.
Determine the probability of playing both sports: We are given that 30 students play both, so P(Cricket ∩ Football) = 30 / 100 = 0.30.
Calculate the conditional probability:
P(Cricket | Football) = (30 / 100) / (50 / 100)
P(Cricket | Football) = 30 / 50
P(Cricket | Football) = 0.60