A. Suppose we have a bag with 10 slips of paper in it. Eight of these have a 2 on them and the other two have a 4 on them.
What is the expected value of the number shown when we draw a single slip of paper?
B. Suppose we have a bag with 10 slips of paper in it. Eight of these have a 2 on them and the other two have a 4 on them.
What is the expected value of the number shown if we add one additional 4 to the bag?
C.Suppose we have a bag with 10 slips of paper in it. Eight of these have a 2 on them and the other two have a 4 on them.
What is the expected value of the number shown if we add two additional 4's (instead of just one) to the bag?
D,Suppose we have a bag with 10 slips of paper in it. Eight of these have a 2 on them and the other two have a 4 on them.
How many 4's do we have to add to make the expected value equal to 3?
E.Suppose I have a bag with 10 slips of paper in it. Eight of these have a 2 on them and the other two have a 4 on them.
How many 4's do I have to add before the expected value is at least 3.5?
+426 Oh My Gosh do you have to repeat whay you are saying?
I'm getting dizzy. Let me rephrase this.
Suppose we have a bag with 10 slips of paper in it. 8 of these have a 2 on them and the other 2 have a 4 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 number 4 to the bag?
c) What is the expected value of the number shown if we add two additional number 4s to the bag?
d) How many 4s to we have to add to make the expected value equal to 3?
e) How many 4s do I have to add before the expected value is at least 3.5?
Cards in bag:
2 2 2 2 2 2 2 2 4 4
a) If we draw a single slip of paper, it is most likely to be a 2.
Thus we have left:
2 2 2 2 2 2 2 4 4
Sum them up to get 22.
22 ÷ 9 = 24/9
b) If we add one more 4, we will have:
2 2 2 2 2 2 2 2 4 4 4
Sum them up, we get 28.
28 ÷ 11 = 23/11
c) If we add 2 more 4s, we will have
2 2 2 2 2 2 2 2 4 4 4 4
Sum them up to get 32.
32 ÷ 12 = 22/3
d)
The sum of all cards = 24
24 ÷ 10 = 2.4
Add a four:
28 ÷ 11 = 2.(54) [1]
Add another four:
32 ÷ 12 = 2.(6) [2]
Keep on adding fours:
36 ÷ 13 = 2.(769230) [3]
40 ÷ 14 = 2.(857142) [4]
44 ÷ 15 = 2.9(3) [5]
48 ÷ 16 = 3 [6]
Answer: 6
e) Keep doing the process above.
52 ÷ 17 = 3.058823... [7]
56 ÷ 18 = 3.(1) [8]
60 ÷ 19 = 3.157894... [9]
64 ÷ 20 = 3.2 [10]
68 ÷ 21 = 3.(238095) [11]
72 ÷ 22 = 3.(27) [12]
76 ÷ 23 = 3.304347... [13]
80 ÷ 24 = 3.(3) [14]
84 ÷ 25 = 3.36 [15]
88 ÷ 26 = 3.384615... [16]
92 ÷ 27 = 3.(407) [17]
96 ÷ 28 = 3.(428571) [18]
100 ÷ 29 = 3.448275... [19]
104 ÷ 30 = 3.4(6) [20]
108 ÷ 31 = 3.483870... [21]
112 ÷ 32 = 3.5 [22]
Answer: 22
