1. Our sample space has 50 students , out of them 15 students took CSE-5301 course and 20 took CSE-5305 course. We know that 10 students are in both classes, based on these information answer the following questions and show the Venn diagram for each one: (7 points each)

• a) how many students are in ether classes?
• b) how many students are in neither classes?
• c) If we randomly select a student, calculate the probability that the chosen student is taking only CSE-5305

2. Suppose we have a fair coin and we toss it 5 times: (5 points each)

• a) Write down the sample space.
• b)what is the probability of getting exactly 2 heads and 3 tails?
• c) What is the probability of getting at least 4 head?

3. Write down the sample space for each one of the following statements? (7.5 points each)

• a) We have a bag containing white and black balls( number of balls are infinite). we keep drawing the balls until we see two white balls (or black balls) in consecutive draw.
• b) We have a bag containing 6 balls (numbered from 1 to 6) we choose 3 balls and save the order of the numbers (calculate the number of items in the sample space, then write down a few example of them).