A factory produces 95% good products and 5% defective products. A quality control test detects a defect 90% of the time for a defective product and 5% of the time for a good product. What is the probability that a product is defective given that it has been flagged as defective by the test?

Two dice are rolled. What is the probability that the sum of the dice is 7, given that the first die shows a 3?

skip all !   A box contains 6 red balls, 3 green balls, and 1 blue ball. If one ball is selected at random, what is the probability that the ball is either red or blue?

A random variable X is uniformly distributed between 0 and 10. What is the probability that X is between 4 and 7?

The number of cars passing through a toll booth follows a Poisson distribution with a mean of 4 cars per minute. What is the probability that exactly 5 cars will pass through the toll booth in a minute?

A jar contains 5 red, 7 blue, and 8 green marbles. If two marbles are drawn one after another without replacement, what is the probability that both are red?

A die is rolled twice. What is the probability that the first roll is an even number and the second roll is a multiple of 3?

The heights of adult women in a population are normally distributed with a mean of 160 cm and a standard deviation of 5 cm. What is the probability that a randomly selected woman has a height greater than 165 cm?

A coin is flipped 3 times. What is the probability of getting at least one head in the three flips?