a)Suppose we have a bag with 8 slips of paper in it. Six of these have a 1 on them and the other two have a 3 on them.

How many 3's do we have to add to make the expected value equal to 2?

b)Problem:
Suppose I have a bag with 8 slips of paper in it. Six of these have a 1 on them and the other two have a 3 on them.

How many 3's do I have to add before the expected value is at least 2.5?

Question

a)Suppose we have a bag with 8 slips of paper in it. Six of these have a 1 on them and the other two have a 3 on them.

How many 3's do we have to add to make the expected value equal to 2?

b)Problem:
Suppose I have a bag with 8 slips of paper in it. Six of these have a 1 on them and the other two have a 3 on them.

How many 3's do I have to add before the expected value is at least 2.5?

anonymous · Answer

2a)Two numbers, x and y, are randomly chosen from the interval [0,1]. What is the expected value of (x+y)?

2b)A line segment is broken at two random points along its length. What is the probability that the three new segments can be arranged to form a triangle?

2c)Three points are selected randomly on the circumference of a circle. What is the probability that the triangle formed by these three points contains the center of the circle?