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 4 to the bag?

c.) What is the expected value of the number shown if we add two additional 4's (instead of just one) to the bag?

d.) How many 4's do we have to add to make the expected value equal to 3?

Lightning
Mar 29, 2018

#1**+2 **

a.) What is the expected value of the number shown when we draw a single slip of paper?

E = (8*2 + 2*4)/(8 + 2) → 2.4

b.) What is the expected value of the number shown if we add one additional 4 to the bag?

E = (8*2 + 3*4)/(8 + 3) → 2.545...

Now try c) and d) yourself.

Alan
Mar 29, 2018

#2**+1 **

Thanks, Alan.....here's the last two

c)

[ 8*2 + 4*4] / [ 8 + 4 ] = [ 16 + 16] / [ 12 ] = 32/12 = 8/3

d) We need to solve this for N

[ 8*2 + N*4] / [ 8 + N ] = 3

[ 16 + 4N] = 3 [ 8 + N ]

16 + 4N = 24 + 3N

N = 8 ⇒ number of 4's we need to have to have an expected value of 3

So....we need to add N - 2 = 8 - 2 = 6

CPhill
Mar 29, 2018