Use the spinner shown. It is equally probable that the pointer will land on any one of the eight regions. If the pointer lands on a borderline, spin again. If the pointer is spun three times, find the probability that it will land on
purple every time
Final Answer: The probability that the pointer will land on purple every time when spun three times is \(\boxed{0.001953125}\).
Step 1 :The problem is asking for the probability of landing on purple three times in a row. Since the spinner has eight regions and each region is equally probable, the probability of landing on purple in one spin is \(\frac{1}{8}\).
Step 2 :Since the spins are independent events, the probability of landing on purple three times in a row is \(\left(\frac{1}{8}\right) * \left(\frac{1}{8}\right) * \left(\frac{1}{8}\right)\).
Step 3 :Calculating the above expression, we get the probability as 0.001953125.
Step 4 :Final Answer: The probability that the pointer will land on purple every time when spun three times is \(\boxed{0.001953125}\).