1.
10% of widgets checked on a production line are found to be faulty. If we select ten items from the production line, find the probability that: a.
3 items are faulty b.
at least 1 item is faulty
(HINT: the sum of all probability outcomes equals 1, find what you don’t need first then . . . )
2.
The office of a large company has recently bought a consignment of ten of the latest photocopying machines for use around the company. The office manager knows from previous experience that there is a 20% probability that any one machine will develop fault within the first twelve months. The cost of repairing such a fault will be, on average, $125. a.
What is the probability that none of the machines will break down in the first year? b.
What is the probability that at least one machine will break down? c.
What is the probability that exactly three machines will break down? d.
How much money should be allocated over the next year to the repair budget for these machines
3.
I have a friend who I wish to check their psychic ability. I decide to use
Zener cards test this. I randomly look at a card without my friend seeing it, and they try to ‘read my mind’ and guess the shape on the card. This is done five times. a.
Show the probability distribution of the possible outcomes (i.e. find
P(X=0), P(X=1), . . . , P(X=6). b.
What outcomes might you want to want to consider your friend being psychic and why?