Statistics and Probability Answers

A financial analyst has found out that, policyholders are four times as likely to file two
claims as to file four claims. If the number of claims led has a Poisson distribution,
what is the expected value of the number of claims led?

A hospital receives 30% of its COVID-19 vaccine shipments from Ghana Health Service
and the remainder of its shipments from neighboring 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 neighboring 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 neighboring West
African countries?

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?

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?

A baseball team has scheduled its opening game for April 5. It is assume that if it
snows on April 5, the game is postponed and will be play on the next day that it
does not snow. The team purchased insurance against snow. The policy will pay GHS
1,000 for each day, up to 2 days that the game is postponed. It is determined that
the number of consecutive days of snow beginning on April 1, is a Poisson random
variable with mean 0.6. What is the expected cost to the nearest one Ghana cedi that
the insurance company will have to pay?

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

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.

The lifetime of a machine is continuous on the interval (0; 40) with probability density
function f, where f(t) is proportional to (t+10)^-2, and t is the lifetime in years. Find
the proportionality constant that makes the f(t) a probability function.

(14). 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?

(4). Suppose Komla throws a die repeatedly until he gets a six. What is the probability
that he needs to throw more than 10 times to get a six, to 3 decimal places?