# How to solve these probability questions [on hold]

1) A piece of equipment functions only when the two components A and B are functioning properly. The probability of component A failing during one year is 0.12 and that of component B failing during one year is 0.03. The functioning state of component A does not influence that of component B. What is the probability that the equipment will fail before the end of the year?

2) Adam celebrates his birthday next month. He intends to send an invitation letter to each of his 10 friends to attend the birthday party. In how many ways can the invited friends receive the invitation letters if Adam has 3 helpers who can each deliver the letters to any of the invited friends?

3)Questions 3 and 4 refer to the following situation: The manager of a large supermarket reported that on average, the supermarket experienced an incident of shoplifting caught by security once every four hours according to a Poisson process.

Suppose the supermarket is open from 9 a.m. to 4 p.m. daily, the probability that more than two shoplifting incidents will be caught by security on a random day is:

4)The probability that the first shop lifting incident will be caught by security after four hours of the supermarket opening for business is:

5)A large non-profit organisation wishes to form an executive leadership team from a group of 6 male executives and 4 female executives. The team will have 5 members. If the team members are selected randomly, what is the probability that the team will have more female executives than male executives?

6)Questions 6 and 7 are based on the following: A company owns a fleet of buses. Half of the buses are in bad state, one third of the buses are just okay and the remaining buses are in good state.

On a trip, a bus in good state breaks down 5% of the time, a bus that is just okay breaks down 20% percent of the time and a bus that is in bad state breaks down 40% of the time. Sipho has travelled once with this bus company and he experienced no breakdowns. The probability that he travelled in a bus that was in good state is:

7)A bus is assigned randomly to each trip. Walter is going to travel four times with this bus company. The probability that he travels exactly twice in a bus that is in good state is:

8)To raise money a school is running a lottery. 1% of all lottery tickets win R1000, 2% of all tickets win R200, 3% of all tickets win R100 and the remaining tickets win nothing.

Which one of the following statements is true?

A. The median amount of money a lottery ticket wins is R150
B. The median amount of money a lottery ticket wins is R200
C. The modal amount of money a lottery ticket wins is R1000
D. The average amount of money a lottery ticket wins is R217
E. The average amount of money a lottery ticket wins is R17

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