Statistics and Probability Answers

Suppose that at a busy traffic junction, the probability p of an individual car having an accident is 0.0001. During a certain part of the day, 100 cars pass through the junction. What is the probability of two or more cars being involved in an accident within this period?

Paula has three keys on a key ring, just one of which opens the door to her
house. As she approaches the door, she selects one key after another, at
random without replacement, trying each key in the door until she finds the
correct key.
(i) Draw up a probability distribution table for X, the number of keys Paula
tries before she opens the door.
(ii) Calculate the expected number of keys that she will try before opening
the door.

The mean number of errors due to a bug occurring in a minute is 0.0001. What is the probability that no error will occur in 20 minutes?

Emmanuel is given a multiple-choice exam with ten questions and each question with five possible answers. He decided to guess randomly for each question. What is the
probability that he will get at least six questions correct?

An archer shoots arrows at a circular target where the central portion of the target
inside is called the bull. The archer hits the bull with probability 1/32. Assume that
the archer shoots 96 arrows at the target, and that all shoots are independent. What
is an approximated probability that an archer hit not more than one bull?

A package of 6 fuses are tested where the probability an individual fuse is defective is
0.05. (That is, 5% of all fuses manufactured are defective). What is the probability
that more than one fuse will be defective, given that at least one is defective?

Suppose that 3% of computer chips produced by a certain machine are defective. The
chips are put into packages of 20 chips for distribution to retailers. What is the
probability that a randomly selected package of chips will contain at least 2 defective
chips?

Suppose that an airline accepted 12 reservations for a commuter plane with 10 seats.
They know that 7 reservations went to regular commuters who will show up for sure.
The other 5 passengers will show up with a 50% chance, independently of each other.
Find the probability that the
flight will be overbooked.

A recent study shows that the annual cost of maintaining a building in Accra averages
200 Cedis with a variance of 260 Cedis. If a tax of 30% is introduced on all items
associated with the maintenance of building i.e. everything is made 30% more expensive.
Calculate the variance of the annual cost of maintaining a building in Accra.

In a bolt manufacturing factory, machines A;B; and C produce 25%, 30% and 45%
of the total output, respectively. Of their outputs, 7%; 6% and 4% are defective bolts,
respectively. If a bolt drawn at random from the production is found to be defective,
what is the probability that it was manufactured by machine C?