please solve this problem without using excel and show all steps

6. A 9-month Asian average price call option on a nondividend paying stock based on arithmetic average of quarterly prices is modeled with a 3-period binomial tree. You are given: (i) The stock price is 49.50. (ii) The strike price is 52. 3 (iii) The tree has u = 1.1, d = 0.9. (iv) The risk free rate is 0.02. Calculate the risk-neutral probability of an option payoff greater than 0