Hello,

Place I need your help for this questions:

1- The passcode of the following consists 6 numbers choosing from 0 ~ 9

A) What is the probability that the passcode has three 9s and 0s?

B) If you already know the code contains at least two 9s, what is the probability that the passcode has three 9s and three 0s?

Hint: a passcode is a sequence of 6 ordered single digit numbers. For example, 999999

2- 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?

3- 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 policyholder has proba-bility 0.001 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.