Question

Indicate clearly the methods you use. Each morning, coffee is brewed in the school workroom by one of three faculty members, depending on who arrives first at work. Mr. Worcester arrives first 10% of the time, Dr. Currier arrives first 50% of the time, and Mr. Legacy arrives first on the remaining mornings. The probability that the coffee is strong when brewed by Dr. Currier is 0.1, while the corresponding probabilities when it is brewed by Mr. Legacy and Mr. Worcester are 0.2 and 0.3, respectively. Mr. Worcester likes strong coffee! What is the probability that on a randomly selected morning the coffee will be strong? Show your work.

Answer 1

To find the probability of the coffee being strong on a randomly selected morning, we need to consider the probabilities of each faculty member brewing the coffee and the corresponding probabilities of it being strong. The probability of the coffee being strong is 0.13 or 13%.

Step-by-step explanation:

To find the probability of the coffee being strong on a randomly selected morning, we need to consider the probabilities of each faculty member brewing the coffee and the corresponding probabilities of it being strong. Let's calculate the probability for each faculty member:

• Mr. Worcester (10% chance) prefers strong coffee (probability = 0.3).
• Dr. Currier (50% chance) brews strong coffee 10% of the time (probability = 0.1).
• Mr. Legacy (40% chance) brews strong coffee 20% of the time (probability = 0.2).

To find the overall probability of strong coffee, we multiply the chances of each faculty member brewing the coffee by the probability of it being strong, and sum them up:

Probability of strong coffee = (0.1 x 0.3) + (0.5 x 0.1) + (0.4 x 0.2)

Therefore, the probability that the coffee will be strong on a randomly selected morning is 0.13 or 13%.