(i) Murphy’s law states that anything that can go wrong will go wrong. The following table lists the joint probabilities of getting a flat tyre while riding your bicycle to work and whether you have an important meeting with your boss.
Have an important meeting with your boss + Flat Tyre 0.66
Have an important meeting with your boss + No Flat Tyre 0.05
Don’t have an important meeting with your boss + Flat Tyre 0.15
Don’t have an important meeting with your boss + No Flat Tyre 0.14
a. Find the probability that you don’t get a flat tyre.
b.Today you have an important meeting with your boss. Determine the probability that you get a flat tyre on the way to work.
c. Are the events independent?
(ii) You’ve decided that instead of cycling to work, it’s safer to drive to work, especially on those days that you have important meetings with your boss. You have decided that it’s much better for the environment if you car pool and pick up three of your work mates on the way to work. If any one of you are running late while getting ready for work, then all four of you will be late for work. Suppose that each person in the carpool has a probability of being on time for work of 0.9 on any one day. Assuming that you all get ready for work independently, what is the probability that you are late for work today?
Please show working because im not really sure on how to go about it. thanks :)
Have an important meeting with your boss + Flat Tyre 0.66
Have an important meeting with your boss + No Flat Tyre 0.05
Don’t have an important meeting with your boss + Flat Tyre 0.15
Don’t have an important meeting with your boss + No Flat Tyre 0.14
a. Find the probability that you don’t get a flat tyre.
b.Today you have an important meeting with your boss. Determine the probability that you get a flat tyre on the way to work.
c. Are the events independent?
(ii) You’ve decided that instead of cycling to work, it’s safer to drive to work, especially on those days that you have important meetings with your boss. You have decided that it’s much better for the environment if you car pool and pick up three of your work mates on the way to work. If any one of you are running late while getting ready for work, then all four of you will be late for work. Suppose that each person in the carpool has a probability of being on time for work of 0.9 on any one day. Assuming that you all get ready for work independently, what is the probability that you are late for work today?
Please show working because im not really sure on how to go about it. thanks :)
-
(i,a) The probability of not getting a flat tire is:
P(no flat tire) = P(no flat tire w/ meeting) + P(no flat w/o meeting)
= 0.05 + 0.14
= 0.19.
(i, b) You are given that:
"Haven an important meeting with your boss + Flat Tire = 0.66,"
so the answer here is 0.66.
(i, c) The events are dependent because having or not having a meeting affects the probability of having a tire and vice-versa.
(ii) The probability that one person will be on time is 0.9, so that all people are on time is (0.9)^4. Thus, the probability that you will be late is 1 - (0.9)^4 = 0.3439.
I hope this helps!
P(no flat tire) = P(no flat tire w/ meeting) + P(no flat w/o meeting)
= 0.05 + 0.14
= 0.19.
(i, b) You are given that:
"Haven an important meeting with your boss + Flat Tire = 0.66,"
so the answer here is 0.66.
(i, c) The events are dependent because having or not having a meeting affects the probability of having a tire and vice-versa.
(ii) The probability that one person will be on time is 0.9, so that all people are on time is (0.9)^4. Thus, the probability that you will be late is 1 - (0.9)^4 = 0.3439.
I hope this helps!