Please show step by step how to calculate the expected inflation rate based on these projections.

Answer: 9.1

Person A projects a 20% probability that inflation will increase to 14.50%

Person B says there is a 35% chance inflation will increase to 9.27%

Person C thinks there is a 45% chance inflation will fall to 6.57%

What is the expected inflation rate based on these projections?

Thank you.