Question

The head chef at a restaurant is purchasing produce for his restaurant's dinner shift. A popular appetizer at the restaurant is melon wrapped in prosciutto. Unfortunately, 6 of the 35 melons on sale are infected with the bacterium Listeria monocytogenes. If the chef randomly selects 3 melons to purchase, what is the probability that all three are free of the dangerous Listeria bacterium?

Answer 1

Total number of melons = 35

Number of infected melons =6

Number of melons free of Listeria bacterium = 35-6 =29.

The chef is randomly selecting 3 melons.

Total number of ways of choosing 3 melons from 35 melons

                             

Number of ways of choosing 3 melons from 29 Listeria bacterium melons

                       

So the probability that all selected melons are free of Listeria bacterium