Refer to the following payoff table:

$\backslash$table$[[$Alternative$,$States of Nature$],[$High$,$Low$],[$Buy$,,60,12],[$Rent$,,19,80],[$Prior$,$Probability,$0\mathrm{.}70,0\mathrm{.}30]]$

There is an option of paying $$100$ to have research conducted to better predict which state of nature will occur. When the true state of nature is High, the research will accurately predict High $75\%$ of the time. When the true state of nature is Low, the research will accurately predict Low $75\%$ of the time.

Given that the research is conducted, what is the joint probability that the state of nature is High and the research predicts Low? Note: Round your answer to $2$ declmal places.

$\backslash$table$[[$Joint Probabilty $,0\mathrm{.}16$