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Total Probability

We have the followings n events {A_1, A_2,....,A_n} that are:

  • they are incompatible events two by two, ie, they haven´t common elements ({A{inter}B=varnothing})

  • if we join all events from E (colection of samples), is the group that is created by all posible results from a random experience.

     That:  {A_1{union}A_2{union}....{union}A_n = E}

Then, the probability of a event S is happened, I can decompose it, as:

tabular{11}{11}{{P(S)=P(A_1)*P(S|A_1)+P(A_2)*P(S|A_2)+....+P(A_n)*P(S|A_n)}}     (Demostration of this result)


A mouse is persecuted by a hungry cat. The mouse can to choose one of these streets A, B or C, to salve himself.

  • The probability that the mouse choose the A street is 0.3 doublerightP(A)=0.3
  • The probability that the mouse choose the B street is 0.5 doublerightP(B)=0.5
  • The probability that the mouse choose the C street is 0.2 doublerightP(C)=0.2

The probabilities that the mouse is hunted by mouse in every street, are:

  • P(cat hunts mouse in A)= P(+|A)= 0.4
  • P(cat hunts mouse in B)= P(+|B)= 0.6
  • P(cat hunts mouse in C)= P(+|C)= 0.1

What´s the probability that cat hunts mouse?.(Calculate P(+))


We make a diagram with tree form to this exercise:

P(+)={(0.3*0.4)+(0.5*0.6)+(0.2*0.1)}=tabular{11}{11}{0.44}   ¡the cat does not have assured the food !LOL

total_probability.txt · Última modificación: 24/04/2017 13:13 (editor externo)
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