Roll two dice Let A denote the event that the sum of the dic

Roll two dice. Let A denote the event that the sum of the dices is 7. Let B denote the event that the first die is 4. Are A and B independent? Why? Suppose 40 percent of the students in a college are female and suppose further that 15 percent of the female and 10 percent of the male students are smokers. We randomly choose a smoker. What is the probability that the smoker is female? We have two boxes, box A containing one black and two white marbles, and box B containing three black and two white marbles. One box is selected at random and a marble is drawn at random from the chosen box. Suppose the selected marble is black, what is the chance that the chosen box is B? Suppose that 30 percent of the bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and remove it from the filling line. If a bottle is not defective, the probability is 0.2 that the inspector will think it is defective and remove it from the filling line. If a bottle is removed from the filling line, what is the probability that it is defective?

Solution

note: We are suppose to answer one question at a time. U have asked 4.

i will give you the solution of 2 and for rest repost the question again.

2) lets us assume there are 100 students

now 40% are female therefore 40 are girls and rest 60 are males.

15% females are smoker therefore 15% of 40 = 6

10% males are smoker so 10% of 60 = 6

total smoker = 12

we choose among smokers and probability the smoker will be female is 6/12