A student $Y$ lives in a place $X$. In $X$ a day can be cloudy with probability $\bf0.02$ uniformly each day. $Y$'s friends may come to his house with probability $\bf0.2$ uniformly in each day irrespective of weather condition. These two events are independent. $Y$ can play or not play in a particular day, and his decision about playing is directly dependent on both the above mentioned two factors. Now the following information is given to you about $Y$'s playing probability on a day.
$P({\text{Y plays}} \; {\bf|} \;\; {\color{maroon}{\text{a cloudy day}},\color{maroon}{\text{friends did not come}} } ) = \bf 0.15$
$P({\text{Y plays}} \; {\bf|} \;\; {\color{maroon}{\text{a cloudy day}},\color{green}{\text{friends came}} } ) = \bf 0.45$
$P({\text{Y plays}} \; {\bf|} \;\; {\color{green}{\text{not a cloudy day}},\color{maroon}{\text{friends did not come}} } ) = \bf 0.65$
$P({\text{Y plays}} \; {\bf|} \;\; {\color{green}{\text{not a cloudy day}},\color{green}{\text{friends came}} } ) = \bf 0.85$
What is the probability of $P({\; \text{Friends came}} \; {\bf|} \;\; {\color{maroon}{\text{Y plays}} } )$ on a particular day ?
