Question

you want to study the respiratory physiology of a certain species of small fish. The pool from whoch you decide to collect the fish has 32 indivisual fish, 8 of which have a fungal infection in their gills. whats the probabilityy that you select 5 fish from this poop and none of them have infected gills?

A.20833

B.00028

C.00000497

D.21107

Answer 1

Answer is (D) 0.21107

Probability of an event = Number of cases favorable to the event / Total number of cases

Here the event is selecting five fish such that none have infected gills

Total number of fish = 32 , Infected gills = 8 , Not infected gills = 32-8 =24

Total number of cases = ³²C₅ = 201376 (its the number of ways 5 fish can be drawn out of 32 fish)

Number of cases favorable to the event = ²⁴C₅ =42504 ( number of ways 5 fish can be drawn out of 24 not infected fish )  

Therefore , Probability of selecting 5 fish such that none have infected gills = 42504 / 201376 = 0.21107