In an aquarium, there are 6 large fish and 8 small fish. Half of the small fish are red. One fish is selected at random. Find the probability that it is a small, red fish.
Write your answer as a fraction.

4/14

Step-by-step explanation:

1/2 of the small fish(8)are red so 4 small red fish out of 8 small fish, then you add the big fish to the denominator(bottom of fraction) and you get 4/14

Both the parts of this question require the use of the "Intersecting Secant-Tangent Theorem".

Part A

The definition of the Intersecting Secant-Tangent Theorem is:

"If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment."

This, when applied to our case becomes, "The length of the secant RT, times its external segment, ST, equals the square of the tangent segment TU".

Mathematically, it can be written as:

Part B

It is given that RT = 9 in. and ST = 4 in. Thus, it is definitely possible to find the value of the length TU and it can be found using the Intersecting Secant-Tangent Theorem as:

Thus,  

Thus the length of TU=6 inches