A piata is a container filled with toys and candy and is broken open by hitting it with a stick. The drawing above shows Sophia trying to break a piata. The probability that she will break the piata on the first hit is 0.7. She will continue to hit the piata until it breaks. If she does not break the piata on a particular hit, the piata is weakened and the probability that she will break it on the next hit is 0.1 greater than the probability on the previous hit. For example, if the piata does not break on the first hit, the probability that it will break on the second hit is 0.8. a) Calculate the probability that Sophia does not break the piata on the first hit and does break the piata on the second hit. b) Let the random variable X represent the number of hits required for Sophia to break the piata. In your answer complete the probability distribution of X in the table below. c) Calculate and interpret the expected value of X. Calculation: Interpretation