Question

A computer program contains one error. In order to find the error, we split the program into 6 blocks and test two of them, selected at random. Let x be the number of errors in these blocks. What is the probability that there are no errors in the tested blocks?

1) 0
2) 1/15
3) 1/6
4) 5/6

Answer 1

The probability of finding no errors in the tested blocks of a computer program, when one error exists among six blocks and two blocks are tested is 2/3 or approximately 0.6667. The given options do not include the correct probability, indicating an error in the provided choices.

Step-by-step explanation:

Calculating the Probability of Zero Errors in Tested Blocks

To calculate the probability that there are no errors in the tested blocks, we must consider that only one of the six blocks contains an error. Since two blocks are being tested, there are C(6,2) or 15 possible combinations of blocks that could be selected. Out of these, the number of combinations where the error is not present in the tested blocks is C(5,2), because we have 5 blocks without errors to choose from. The probability of selecting a combination without the error is therefore the number of combinations without the error divided by the total number of combinations. This gives us:

P(x = 0) = C(5,2) / C(6,2) = 10 / 15 = 2/3 or approximately 0.6667, which is not an option provided in the question. This implies that there was an error in the options given, as "2/3" or "4/6" is the correct calculation for this scenario.