1. There are 4 golden coins and 8 iron coins in a bag. You select one coin from the bag, if it is a golden coin, you keep it; but if it is an iron coin, you put it back in the bag. Find the probability of earning exactly 2 golden coins after:
2. Two consecutive selections
3. Three consecutive selections

1. For David, the probabilities of passing Course A, Course B, and Course C are 0.7, 0.8, and 0.6, respectively. Assuming that passing or failing a course does not affect any other course's success, what is the probability that David will fail at least two courses?

1. Let A and B be two independent events in a sample space, S. If P(AB)=0.16 and P(AB)=0.64, then find P(A) and P(B).

1. In a trial of rolling 2 dice, if it is known that the numbers on the dice are different, then what is the probability that the product is odd?

1. In a multiple-choice exam, there are 20 questions, each of which has 5 choices. From these 5 choices, only one choice is the correct answer and the rest are incorrect answers. A lazy student answers all questions randomly regardless of correctness; that is, the student makes a random choice without reading and understanding the question.
   1. Explain why this is a Binomial problem.
   2. Find the probability that the student answers all questions correct.
   3. Find the probability that the student answers all questions incorrect.
   4. If answering 10 questions correct is enough to pass the course, find the probability that the student passes the course.

1. The table shows a random sample of 500 students accepted to different programs of a college.

	Computer Science	Social Science	Healthcare	TOTAL
Female	65	70		286
Male	120			214
TOTAL		95	220	500

1. Complete the table.
2. What is the percentage of students who are accepted to social science and female?
3. What is the percentage of students who are accepted to social sciences are female?
4. What is the percentage of students who are accepted healthcare or computer science?
5. What is the percentage of male students who are accepted to healthcare?
6. What is the percentage of computer science students who are female?