Problem of the Week - Algebra and Up - Feb. 28, 2021 to March 6, 2021

Algebra and Up: 

Question: Dave, Tom and Star agree to meet at "the coffee shop by the park." Unfortunately, there are three coffee shops by the park, and they forget to specify which one. What is the probability that Dave, Tom and Star will all go to different coffee shops? 

Answer: 2 out of 9

Solution: Dave has a ¹/₁ probability of going to whichever coffee shop he goes to. Tom then has a ²/₃ probability of going to either of the two coffee shops where Dave didn’t go. If that happens, then there’s a ¹/₃ probability that Star will go to the remaining coffee shop. So, the probability that they all go to different coffee shops is ¹/₁ × ²/₃ × ¹/₃ = ²/₉