An insurance company receives two type of claims: car and home. The number of car insurance claims received follows a Poisson distribution with rate 20 claims per day. The number of home insurance claims received follows a Poisson distribution with rate 5 claims per day. Assume the number of home insurance claims and the number of car insurance claims submitted are independent. (a) Find the probability of the total number of claims submitted per day is at most 20. (b) How many claims all together the company expect to receive in a period of 30 days