Question

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 $9$ on them. How many $9$’s do we have to add to make the expected value equal to $6$

1. Value of the given statement:
1. 4.36
2. 5
3. 6
4. 38

### What is Probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event’s impossibility and 1 denotes its certainty.
According to the given information:
1) There are a total of 10 slips after adding.
8 slip with 3 on it
2 slips with 9  on it
value = Probability of 3 x 3 plus Probability of 9 x 9.
=  (8 / 11)  x 3 + (2/ 11)  x 9
24 / 11 + 24 / 11 = 4.36
2 )No of total slips after addition = 12
8 slip with 3 on it
4 slips with 9  on it
value = Probability of 3 x 3 plus Probability of 9 x 9.
=  (8 / 12)  x 3 + (4 / 12)  x 9
2 + 3 = 5
3 )Let n be the required number
No of total slips after addition = 10+n
8 slip with 3 on it
2 + n  slips with 9  on it
value = Probability of 3 x 3 plus Probability of 9 x 9.
=  (8 / 10+n )  x 3 + (2+n  / 10+n )  x 9 = 6
24 + 18 + 9n / 10 + n  = 6
42 + 9n = 60 + 6n
3 n = 18
n = 6
4 )Let n be the required number
No of total slips after addition = 10+n
8 slip with 3 on it
2 + n  slips with 9  on it
expectation value = probability of 3 x 3 + probability of 9 x 9
=  (8 / 10+n )  x 3 + (2+n  / 10+n )  x 9 = 8
24 + 18 + 9n / 10 + n  = 8
42 + 9n = 80 + 8n
n = 38
Minimum of 38 has to be added .
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I understand that the question you are looking for is:
1: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 $9$ on them. What is the expected value of the number shown if we add one additional $9$ to the bag? 2: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 $9$ on them. What is the expected value of the number shown if we add two additional $9$’s (instead of just one) to the bag? 3: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 $9$ on them. How many $9$’s do we have to add to make the expected value equal to $6$? 4: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 $9$ on them. How many $9$’s do I have to add before the expected value is at least $8$?