A company has 100 employees. 70 speak English, 45 speak French, and 10 speak neither. If an employee is chosen at random and is known to speak English, what is the probability that they also speak French?
Answer and explanation
Correct answer: B. 5/14
- Step 1: By inclusion-exclusion: Total = E + F - Both + Neither.
- Step 2: 100 = 70 + 45 - Both + 10 = 125 - Both, so Both = 25.
- Step 3: We want the conditional probability P(F | E) = Both / E.
- Step 4: P(F | E) = 25 / 70 = 5 / 14.
Answer
5/14.
Why not the others: 1/4 computes 25/100 (unconditional probability); 1/2 computes 35/70; 9/20 computes 45/100.
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