The firm can interpret the soil test by using Bayes’ Theorem to see what the posterior probabilities of seeing different of oil as wlel as no oil are. By using this, you can tell that it’s more likely that they are going to find medium quality oil.
P(E1soil)= .5*.2=.1
P(E2 soil)=.2*.8=.16
P(E3soil)=.3*.2=.06
P(soil)=.1+.16+.06=.32
P(E1|soil)=.1/.32=.3125
P(E2|soil)=.16/.32=.5
P(E3|soil)=.06/.32=.1875
P(Oil)=P(medium quality oil high quality oil)=.3125+.5=.81257
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great rest of Black History Month! :-)
- Cutiepatutie ☺❀❤
The new probability of finding oil is 0.81257.
Bayes’ Theorem
The firm can interpret the soil test by using Bayes’ Theorem to see what the posterior probabilities of seeing different oil, as well as no oil, are. By using this, you can tell that it’s more likely that they are going to find medium-quality oil.
P([tex]E_{1}[/tex] |soil) [tex]= 0.5*0.2=0.1[/tex]
P([tex]E_{2}[/tex] |soil) [tex]=0.2*0.8=0.16[/tex]
P([tex]E_{3}[/tex] |soil) [tex]=0.3*0.2=0.06[/tex]
P(soil) [tex]=0.1+0.16+0.06=0.32[/tex]
P([tex]E_{1}[/tex] |soil) [tex]=0.1/0.32=0.3125[/tex]
P([tex]E_{2}[/tex] |soil) [tex]=0.16/0.32=0.5[/tex]
P([tex]E_{3}[/tex] |soil) [tex]=0.06/0.32=0.1875[/tex]
P(Oil) = P(medium quality oil | high-quality oil)
[tex]=0.3125+0.5=0.81257[/tex]
Therefore, the new probability of finding oil is 0.81257.
To learn more about Bayes’ Theorem
https://brainly.com/question/14989160
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