Statistics and Probability Answers

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?

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

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
ight will be overbooked.

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?

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?

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

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?

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.