Let A and B be events such that P (A) = 4/10 and that P (A∪B) = 7/10  Find the probability of B assuming that A and B are independent.

A commuter must pass through three traffic lights on her way to work. For each traffic light, the probability that it is green when she arrives is 0.6. The lights are independent. 3 (a) Compute the probability that all three lights are green. (b) The commuter goes to work five days per week. Let X be the number of times out of the five days in a given week that all three lights are green. Assume the days are independent of one another. Determine the distribution of X. (c) Calculate P(X= 3).

A bag contains 10 Blue balls, 10 Red balls, and 9 Green balls. Two balls are going to be drawn from the bag (one at a time) and then put to the side (they are not returned to the bag). Let event B blue ball chosen, R = Red ball chosen, and G- Green ball chosen. What is the probability they are both red? What is P(R and R)? Write an answer to 4 decimal places.

The probability that a student at a university is a male is 0.48, that a student is a business major is 0.14 and that a student is a male and a business major is 0.06. Find the probability that a randomly selected student from this university (a) is a male or business major. (b) is a male given that he is a business major. (c) is either a male or a business major but not both. (d) is neither male nor business major. (e) Are male and business major independent events?

A certain disease has a prevalence of in a population. The rate of false 4 positives is 10% and and the rate of false negatives is 5%. If you are exposed to the disease, then probability that you contract it is . You can only contract the disease by sharing food. Suppose that you meet 10 people, that each person tests negative for the disease, and that you share food with each of them exactly three times. What is the probability that you contract the disease?

Let A and B be two events such that the probability of B is 0.5 and the probability of both is 0.2. Find the probability of A given that B occurs.

Assume for this problem that the company has 8 BMWs and 5 Hondas, and two cars are selected randomly and given to sales representatives. What is the probability of both cars being BMWs, given that both are of the same make?

a and b

A company receives 30% of its shipments from source A and the rest from source B. For source A, the defective rate is 10% and for source B, the defective rate is 6%. The company just receives a shipment which contains 10 items.Determine the probability that there will be one defective item.