Consider Bob's decision problem:

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & Sunny & Cloudy & Rainy $\backslash \backslash$

$\backslash$hline Beach & $2$ & $3$ & $2\backslash \backslash$

$\backslash$hline Park & $3$ & $3$ & $2\backslash \backslash$

$\backslash$hline Mall & $2$ & $3$ & $4\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Suppose the probability of Sunny is $0\mathrm{.}1,$ the probability of Cloudy is p and the probability of Rainy is $\backslash (1-0\mathrm{.}1-\backslash$mathrm$\{$p$\}\backslash ).$ What the largest value of $\backslash ($ p $\backslash )$ for which Mall maximises Bob's expected utility $($that is$,$ Mall is at least the equal$-$best choice$)?$ Round your answer to two decimal places $($e$.$g$.0\mathrm{.}55).$