Statistics and Probability Answers

Giving a test to a group of students, the grades and gender are summarized below

A B C Total
Male 17 8 5 30
Female 18 19 3 40
Total 35 27 8 70


If one student is chosen at random,

Find the probability that the student was female OR got an "B".

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

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

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

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

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 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 2 baskets, 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 discrete random variable has probability mass function, P(X = n) = =
1
2

n
.
Let Y =

1, for x even
n1, for x odd
Find the expected value of Y ; (E[y]).

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?