Probability about a geometric distributionIf no-one obtains "head", the game continues with the same probabilities as before." If that is the case, why does that affect the probability recursively? Could someone explain why we add the case where no one wins to the probability, and why we multiply it by p?

Question

Probability about a geometric distributionIf no-one obtains &quot;head&quot;, the game continues with the same probabilities as before.&quot; If that is the case, why does that affect the probability recursively? Could someone explain why we add the case where no one wins to the probability, and why we multiply it by p?

uiteensitnh · Accepted Answer

Step 1The game has three states:S:  So far nobody has thrown heads,M: Mary has thrown heads,M′:     ≥  1 of the boys has thrown heads, but Mary hasn&#039;t.Step 2M and M′ are terminal states with assigned probabilities 1 and 0 that Mary wins the game. Let p denote the probability that Mary wins when we are in state S. The transition probabilities between the three states are as follows:                    S        →        M        :                                      p          2                                    S        →                  M          ′                :                            (        1        −                  p          2                )        (                  p          1                +                  p          3                −                  p          1                          p          3                )                            S        →        S        :                            (        1        −                  p          1                )        (        1        −                  p          2                )        (        1        −                  p          3                )            Looking at the flow-chart we see that p satisfies the equation   p  =      p    2    ⋅  1  +  (  1  −      p    1    )  (  1  −      p    2    )  (  1  −      p    3    )  ⋅  p     , as given in Joriki&#039;s answer.

If no-one obtains "head", the game continues with the same probabilities as before." If that is the case, why does that affect the probability recursively? Could someone explain why we add the case where no one wins to the probability, and why we multiply it by p?

Answered question

Answer & Explanation

New Questions in High school geometry