Question

The probability of a defective steel rod is 0.01. Steel rods are selected at random. Find the probability that the first defect occurs on the ninth steel rod.

Answer 1

Answer:

We can solve the problem by using Geometric Distribution.

Let X = the total number of components to be tested (theoretically infinite)

Given that;

The probability of a defective steel rod P(D) = 0.01

Also given that;

The defect needs to occur at 9th steel rod

Hence, to find the probability that the defect occurs at X=9, we need to find P(X=9) with p = 0.01

Using T1-84 calculator,

P(X=9) = 0.009

Step-by-step explanation:

Steel rods are picked at random and the count of the steel rods is unspecified. So, keeping aside the practical occurrences, in theory, the number of times the that steel rods could be picked is infinite (X = 1,2,3,…. ) and where the rods are picked at least once because the question states so.

So, here we can solve P(X=9) by using T1-83 (or) T1-83+ (or) T1-84 (or) T1-84+ calculator.

Steps to use the calculator to find P(X=9):

• Enter 2nd, DISTR

• Scroll down and select geometpdf(

• Press ENTER

• Enter 0.01, 9); press ENTER to see the result: P(x = 9) = 0.009