An insurance company hands out flyers on which customers leave their contact e-mail so that the insurance company can contact them later. These flyers are transcribed to a computer system. In the data entry operation, a typist reads the handwriting from the flyer. In 95 percent of the cases, the handwriting is read correctly. In 0.5 percent of the cases, the typist makes a mistake and writes something different from what he had read on the flyer. Create an event tree. What is the probability that the data are entered correctly?

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An insurance company hands out flyers on which customers leave their contact e-mail so that the insurance company can contact them later. These flyers are transcribed to  a computer system. In the data entry operation, a typist reads the handwriting from the flyer.   In 95 percent of the cases, the handwriting is read correctly. In 0.5 percent of the cases, the typist makes a mistake and writes something different from what he had read on the flyer.   Create an event tree. What is the probability that the data are entered correctly?

chumants6g · Accepted Answer

Step 1  Given: In the data entry operation, a typist reads the handwriting from the flyer. In 95 percent of the cases, the handwriting is read correctly. In 0.5 percent of the cases, the typist makes a mistake and writes something different from what he had read on the flyer.  Data entered correctly⇒(Data read correctly)(Data written correctly)  The probability that data is read correctly: 95%=0.95  The probability that data is written incorrectly: 0.5%=0.005  Therefore, the probability that data is written correctly: 1−0.005=0.995  Step 2  Now, the probability that data is entered correctly:  P(data entered correctly)=P(data read correctly)×P(data written correctly)  =0.95×0.995  =0.94525  Thus, the probability that data is entered correctly is 0.94525.

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