+0

# Expected value

+1
54
1

I need help with these

Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have a 5 on them.

(a) What is the expected value of the number shown when we draw a single slip of paper?
(b) What is the expected value of the number shown if we add one additional 3 to the bag?
(c) What is the expected value of the number shown if we add two additional 3's (instead of just one) to the bag?

Mar 29, 2023

#1
+1

(a): there is a 8/10 probability of pulling a 3 and a 2/10 probability of pulling a 5 so the expected value is $$\frac{8}{10}(3) + \frac{2}{10}(5)$$ Expected value for drawing one slip of paper, this is equal to 3.4 or 34/10 or 17/5

(b): well, this would be the exact same idea except the probabilities are different, now the expected value is $$\frac{9}{11}(3) + \frac{2}{11}(5)$$ which simplifies to 37/11

(c): Once again, same idea, the expected value would be $$\frac{10}{12}(3) + \frac{2}{12}(5)$$ which simplifies to 10/3

If you have any questions, just ask :)

Mar 29, 2023