In a survey, 70% of people like tea and 40% like coffee. If 30% like both, what is the probability that a person likes coffee given that they like tea?
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In a survey, 70% of people like tea and 40% like coffee. If 30% like both, what is the probability that a person likes coffee given that they like tea?
Q: In a survey, 70% of people like tea and 40% like coffee. If 30% like both, what is the probability that a person likes coffee given that they like tea?
Step 1: Understand the problem. We need to find the probability that a person likes coffee given that they like tea.
Step 2: Identify the information given in the problem. We know that 70% of people like tea (P(T) = 0.7), 40% like coffee (P(C) = 0.4), and 30% like both tea and coffee (P(C ∩ T) = 0.3).
Step 3: Use the formula for conditional probability. The formula is P(C|T) = P(C ∩ T) / P(T).
Step 4: Plug in the values we have. We know P(C ∩ T) = 0.3 and P(T) = 0.7.
Step 5: Calculate P(C|T). So, P(C|T) = 0.3 / 0.7.
Step 6: Simplify the fraction. 0.3 / 0.7 = 3/7.
Step 7: Conclude that the probability that a person likes coffee given that they like tea is 3/7.
