In a survey, 70% of people like tea, and 40% like coffee. If 30% like both tea and coffee, what is the probability that a person likes tea given that they like coffee?
Practice Questions
1 question
Q1
In a survey, 70% of people like tea, and 40% like coffee. If 30% like both tea and coffee, what is the probability that a person likes tea given that they like coffee?
0.5
0.7
0.3
0.4
Using conditional probability, P(Tea | Coffee) = P(Tea and Coffee) / P(Coffee) = 0.3 / 0.4 = 0.75.
Questions & Step-by-step Solutions
1 item
Q
Q: In a survey, 70% of people like tea, and 40% like coffee. If 30% like both tea and coffee, what is the probability that a person likes tea given that they like coffee?
Solution: Using conditional probability, P(Tea | Coffee) = P(Tea and Coffee) / P(Coffee) = 0.3 / 0.4 = 0.75.
Steps: 7
Step 1: Understand the problem. We want to find the probability that a person likes tea given that they like coffee.
Step 2: Identify the information given in the problem. We know that 30% of people like both tea and coffee (this is P(Tea and Coffee)), and 40% like coffee (this is P(Coffee)).
Step 3: Use the formula for conditional probability. The formula is P(Tea | Coffee) = P(Tea and Coffee) / P(Coffee).
Step 4: Substitute the values into the formula. We have P(Tea and Coffee) = 0.3 and P(Coffee) = 0.4.
Step 5: Calculate the probability. So, P(Tea | Coffee) = 0.3 / 0.4.
Step 6: Perform the division. 0.3 divided by 0.4 equals 0.75.
Step 7: Conclude that the probability that a person likes tea given that they like coffee is 0.75.
