1- A fencer attends a fencing tournament. To ensure the equipment works well, he takes three blades. Two of them will be the backup. The probability of his three blades to function properly are 0.95, 0.8, 0.7 respectively.
A) Find the probability that the fencer finishes the tournament with at leaset one working blade?
B) Find the probability that the fencer has one and only one working blade during the tournament?
2- An insurance e company issues life insurance policy in three categories: stan- ard preferred and ultra - preferred. Of the company's policyholders 50 % are standard, 30% are preferred and 20% are ultra-preferred. Each standard policyholder has proba-bility 0.010 of dying in the next year, each preferred policyholder has probability 0.005 of dying in the next year, and each ultra-preferred policyholder has probability 0.001 of dying in the next year.
A policyholder dies in the next year.
Calculate the probability that the deceased policyholder was ultra-preferred.