The manager at Mugg & Bean has been recording the behaviour of their customers with regards to coffee and muffins. The manager established that that the probability that a customer will buy a cup of coffee is 0.8. A customer buys a muffin 50% of the time when a cup of coffee is bought, but only 10% of the time when a cup of coffee is not bought. What is the probability of buying a cup of coffee and a muffin (rounded off to two decimals)?
To find the probability of buying a cup of coffee and a muffin, we need to multiply the probabilities of each event happening.
Let's assign some variables:
A = Buying a cup of coffee
B = Buying a muffin
Given information:
P(A) = 0.8 (probability of buying a cup of coffee)
P(B|A) = 0.5 (probability of buying a muffin given that a cup of coffee is bought)
P(B|¬A) = 0.1 (probability of buying a muffin given that a cup of coffee is not bought)
To find P(A and B), we can use the formula:
P(A and B) = P(A) * P(B|A)
Using the given information, we have:
P(A and B) = 0.8 * 0.5
P(A and B) = 0.4
Therefore, the probability of buying a cup of coffee and a muffin is 0.4 or 40% (rounded off to two decimal places).