Question

A pearl diver goes from clam to clam, checking to see if a pearl is inside. Suppose 10% of clams contain a pearl inside. Approximate the chance that the diver has to check less than 175 clams in order to find his 15th pearl.

Answer 1

The diver will check fewer clams to find his 15th pearl. He will check 15 clams which is 2 clams less than the 17 clam chance given by the 10% probability.

Explanation:

CLAM

This is a marine animal that has two shells and live by straining food from water, sand, or mud. They can sometimes found by digging the sand close to the seashore. Like mussels, they can produce pearls, but not as often.

PEARL

They are gems that come in various colors like white, red, gray, blue, green, and black. They are very beautiful and are typically spherical, some also come in an uneven form such as the baroque pearls.

The probability of find pearl inside a clam according to the question is 10%.

P (find pearl in clam) =
`(10)/(100)` =
`(1)/(10)`

If we have to check 175 clams to look for pearls, how many clams are we expected to search in other to find pears given a 10% probability out of 175

P (clam with pearl)=
`(175*1)/(10)` =17.5

Which is approximately 17 clams

For the diver to find his 15th pearl, he has to check with a minimum chance of checking 15 clams. But the 10% probability of finding a pearl inside a total of 175 clams is 17 clams.

This means the diver will check fewer clams to find his 15th pearl.