Statistics and Probability Answers

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?

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?

Suppose a ball is drawn at random from a box containing three white and three black
balls. After a ball is drawn, it is then replaced and another drawn. What is the
probability that of the first four balls drawn, exactly two are white?

A hospital receives 30% of its COVID-19 vaccine shipments from Ghana Health Service
and the remainder of its shipments from neighbouring West African countries. Each
shipment contains a very large number of vaccine vials. For GHS’s shipments, 8% of the
vials are ineffective and for the neighbouring countries, 3% of the vials are ineffective.
The hospital tests 30 randomly selected vials from a shipment and finds that one is
ineffective. What is the probability that the shipment came from neighbouring West
African countries?

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?

Emmanuel is given a multiple choice question 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.

Raymond is a basketball player who takes four independent free throws with 70% probability of getting a basket on each shot. Let X be the number of baskets Raymond gets. Find the probability that he gets exactly 2 baskets, to 3 decimal places.

Raymond is a basketball player who takes four independent free throws with 70% probability of getting a basket on each shot. Let X be the number of baskets Raymond gets. Find the probability that he gets exactly two baskets, correct to 3 decimal places.

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.

A random variable X has a Poison distribution with mean equal to 0.4. What is the probability the probability that the random variable is greater than zero.