Formating instructions: For all answers in Q$2-14,$ please write their decimal values rounded to four decimal places. We consider an answer correct if and only if it differs no more than $0\mathrm{.}0001$ from the solution.

ALL BELOW QUESTIONS ARE RELATE TO ABOVE FIGURE SHOW ALL STEPS

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QUESTION $2$

Compute P$($c $=1).$

QUESTION $3$

Compute P$($f $=1)$

QUESTION $4$

Compute P$($f $=1|$ a $=1)$

QUESTION $5$

Compute P$($f $=1|$ c $=0)$

QUESTION $6$

Compute P$($f $=1|$ a $=1,$ b $=1)$

QUESTION $7$

Compute P$($f $=1|$ a $=1,$ b $=1,$ c $=1)$