Discussion
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 ?
Answer: C
The probability is 0.60.
Given that the student plays football, we look only at the 50 football players, of whom 30 also play cricket:
\[ P(C \mid F) = \frac{30}{50} = 0.60 \]
0.30 is the unconditional probability of playing both (30 out of 100), and 0.15 and 0.18 do not follow from the figures.
The general rule is P(C | F) = P(C and F) / P(F) = 0.30 / 0.50, which gives the same 0.60.
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