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 $6$

Answers

  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 $8$?

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