3) In a factory, there are 100 new cars produced. Three of the cars have serious defects. The quality control group is going to select 10 cars at random and check them thoroughly. (Each car has same probability than the others to get selected). If in the ten controlled cars they find at least one with a defect, they will control the whole group of 100. What is the probability that they will end up checking the whole bunch? (We assume that when they check a defect car, they always discover that the car is defect.)

A box contains 20 marbles: 5 blue, 10 red, and 5 orange. Suppose we take a sample of size 5. What is the chance that we see 1 blue, 2 red, and 2 orange?

According to Mendel’s theory, if tall and colorful plants are crossed with short and colorless plants, the corresponding probabilities are 9/16, 3/16, 3/16, and 1/16 for tall and colorful, tall and colorless, short and colorful, and short and colorless, respectively. If 8 plants are selected, find the probability that 1 will be tall and colorful, 3 will be tall and colorless, 3 will be short and colorful, and 1 will be short and colorless.(4 decimal digits)

There are three containers, A, B and C. Each container contains 25 balls, which are either red or blue. Container A has 15 red balls, container B has 16 red balls, and container C has 12 red balls. In a random experiment, one first randomly chooses a container, and then a ball is drawn from the chosen container. The probability of choosing container B in step 1 is 2/5 . The experiment is designed so that the events “the ball drawn is red” and “the ball drawn comes from container A” are independent. Suppose that the ball drawn is red. What is the probability that it came from container C?

In 2013, the total sales from 3 different car production companies was 606,334 cars or light trucks. The probability that the vehicle was made by Company A was 0.381, by Company B 0.350, and by Company C 0.258. Additionally, the probability that a Company A vehicle sold was a car was 0.385, a Company B vehicle sold was a car was 0.370, and a Company C vehicle sold was a car was 0.332. Given the vehicle sold was a car, find the probability it was made by Company A. The probability a vehicle was made by Company A, given it was a car is (Round to three decimal places as needed.)

The vast majority of European vehicles sold in the world (BMW, Audi, Mercedes- Benz, etc...) receive their transmissions from either ZF Friedrichshafen AG or Continental AG. After the acquisition of TRW by ZF, ZF AG supplied 69% of transmissions, and Continental AG supplied 31%. If three European cars are randomly selected, what is the probability that 2 of the cars use ZF transmissions and 1 use Continental AG transmission? Enter your answer in percent terms (for example 12.5% must be entered as 12.5).

Suppose that the population is 1000 people and the probability of cat people is 25% if we take a random sample of 100 people what is the probability that the proportion in the sample will be bigger than 29%

A shipment contains 12 igneous, 10 sedimentary, and 10 metamorphic rocks. If 5 rocks are selected at random, find the probability that exactly 3 are sedimentary. The probability that exactly 3 of the rocks are sedimentary is (Round to four decimal places as needed.)

A survey from Teenage Research Unlimited found that 40% of teenage consumers receive theirspending money from part-time jobs. If 5 teenagers are selected at random:a. Find the probability that at least 3 of them will have part-time jobs.b. Find the probability that no more than 4 will have part-time jobs.c. Find the probability that less than 5 but greater than 3 will have part-time jobs.

Consider a group of 8 people. Among them, there is one pair of twins. These 8 people are taken into two different rooms, Room A and Room B, with four people to each room. If all  groups of four people are equally likely, find the probability that the twins will be sent into the sameroom.