# Tricky question

Q. By the rule of seven, a process is said to be out of control if a run of seven samples is found on one side of the process mean. What is the probability that a run of seven occurs on either side of the mean due to random variation?

• 0.02

• 0.035

• 0.0156

• 0.0273

Explanations:

Answer (c) 1.56% . Correct Answer is 'C'. Let the first sample be on any one side of the mean. The probability that the subsequent sample is on the same side is A, the probability that the third sample is on the same side is again 1/2 A, and so on. The probability for the seventh sample on the same side is also A. Therefore the probability that all the six subsequent points is on the same side as the first is 1/2A * 1/2A * 1/2A * 1/2A * 1/2A * 1/2A = 1/64 = 0.0156 => 1.56%.

Can anybody explain why are we not taking 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128?

### I did not find a solution

I did not find a solution myself, but it is quite evident now.

It is like a roulette. 1/2 (random) is a probability to get red as a result of 1 spin. To get the probability of 7 consequent times red you need to multiply the probabilities of every spin 7 times.

Imagine heads and tails game - how easy is to get 7 times tale.

### Not relevant to exam...!!!

Such type of questions will not appear in actual exam.

The PMP exam is designed to test one's PM's knowledge rather than Statistical Analysis.

I did not find such question in any Mock as well as in actual exam.

EVM is the most important calculative topic for PMP exam.

### Relevance

This question is from one of the mocktests of simplilearn. The relevance in project management is that this a typ2 error (beta risk) - risk of accepting a false alternate hypothesis which comes under project risk management.