We are given that a computer manufacturing company sampled two different parts and tested for defects. Let's see the results in the following two-way frequency table.
Part A
Part B
Defective
14
33
Not defective
266
312
We want to find the probability that a randomly chosen part is defective if it is a Part B. In other words, a favorable outcome is a defective Part B, given that the part is a Part B. Since we can assume that the part has already been determined to be a Part B, we will use the Conditional Probability Formula.
To apply this formula, we will first find the probability that a Part B is randomly chosen. To do so, we will calculate the ratio of the total number of Part B parts to the total number of parts available.
P( Part B)=33+ 312/14+ 266+ 33+ 312 ⇒ 345/625
Next, we will find the probability that a randomly chosen part is a defective Part B. Note that 33 items are both defective and from Part B. Let's write out this probability as the ratio of those 33 items to the total number of items 625.
P( Defective Part B)=33/625
Great! Now, we can find the ratio of those two probabilities to calculate the result of our conditional probability.
P(Defective | Part B)=P(Defective and Part B)/P(Part B)
