You prefer to use credit cards instead of cash, but the new anomaly detection technology is far from foolproof - it makes one false detection for every nine purchases made by swiping your card. You expect to make three purchases today. Assume that each purchase is an independent event.

What is the probability of zero false detections?

Under the same assumptions, what is the probability ofat leastonepurchase triggering false detections?

Let X be the number of false detections (X = 0, 1, 2, or 3) and assume that you make three purchases using your credit card.Create a probability distribution for X (Hint: Draw a tree diagram to calculate the probabilities for each value of X. Show how you arrived at these probabilities. Present the probability distribution)Round your answers to the fourth decimal point.

What is the probability of gettingat mostone false detection?

What is the mean of X?

What is the standard deviation of X?