Math Help - posterior probability question

1. posterior probability question

hi
in the attachment is the question
I have problem solving it
from question I just knew the Prior Probability for that their claim correct is =0.2 and not correct =0.8
after he did the experiment he found that it is correct 100 %
but I could not find where is the posterior
Prior Probability =0.2
correcting information= 1
posterior =?
until now this is what I came up with

2. Originally Posted by Logical
hi
in the attachment is the question
I have problem solving it
from question I just knew the Prior Probability for that their claim correct is =0.2 and not correct =0.8
after he did the experiment he found that it is correct 100 %
but I could not find where is the posterior
Prior Probability =0.2
correcting information= 1
posterior =?
until now this is what I came up with

Prior: Pr(T > 10) = 0.2

Pr(Data | T > 10) = 1, Pr(Data | T < 10) = 0.

$\Pr(T > 10 \, | \, \text{Data}) = \frac{\Pr(T > 10 \cap \text{Data})}{\Pr(\text{Data})}$.

$\Pr(T > 10 \cap \text{Data}) = \Pr(\text{Data} \, | \, T > 10) \cdot \Pr(T > 10) = (1) (0.2) = 0.2$.

$\Pr(\text{Data}) = \Pr(\text{Data} \, | \, T > 10) \cdot \Pr(T > 10) + \Pr(\text{Data} \, | \, T < 10) \cdot \Pr(T < 10)$ $= (1)(0.2) + (0)(0.8) = 0.2$.

Therefore $\Pr(T > 10 \, | \, \text{Data}) = \frac{0.2}{0.2} = 1$.

3. Thank you for helping me