Question

A pond is freshly stocked with 6 brown trout and 18 lake trout. The first fisherman in the area catches and releases a trout. He catches another trout a while later. What is the probability that the fisherman caught lake trout each time?

A.1/16

B.1/8

C.5/92

D.5/96

Answer 1

9/16

Not given in the options.

Explanation:

Probability is the number of possible outcome expressed as a fraction of the total outcome.

Number of brown trout = 6

Number of lake trout = 18

Total number of trout = 18 + 6 = 24

Probability of picking a brown trout = 6/24

Probability of picking a lake trout = 18/24

The probability of picking a lake trout twice (with replacement)

= 18/24 × 18/24

= 9/16

Not given in the options.

Answer 2

Number of brown trout = 6

Number of lake trout = 18

Total number of trouts =
`6+18=24`

Probability to catch a lake trout first time =
`(18)/(24)`

As the fisherman let the trout go, so probability for the second time is =

`(18)/(24)`

Hence, the probability becomes=

`(18)/(24)*(18)/(24)=(324)/(576)`

=
`(9)/(16)`

The probability to find the brown trout is
`(1)/(16)`

as ,
`(6)/(24)*(6)/(24)=(36)/(576)`

=
`(6)/(96)=(1)/(16)`