Write an equation before solving for a game probability

Let X count wins among 20 games; under the source constant-p independent-game model, $X\sim B(20,p)$. Then $P(X\ge2)=0.06$, so $1-P(X\le1)=0.06$. The source expansion is $1-\binom{20}0p^0(1-p)^{20}-\binom{20}1p^1(1-p)^{19}=0.06$, giving $1-(1-p)^{20}-20p(1-p)^{19}=0.06$.

Enter the left-hand expression as Y1 and 0.06 as Y2. Adjust the window to show the intersection, then use the calculator’s intersection command: its x-coordinate is p. The printed window is Xmin 0, Xmax 0.2, Xscl 5, Ymin 0.01, Ymax 0.1, Yscl 0.25, Xres 1 (derived ΔX≈0.000757576, TraceStep≈0.00151515). The numerical result is $p\approx0.02001912$, hence 0.0200 to 3 significant figures. The source alternative is to plot $y=1-(1-p)^{20}-20p(1-p)^{19}-0.06$ and find its x-intercept.

The source remark requires an explicit equation from the MF27 probability formula when asked to “write down an equation”. The Teacher warns against the integer-table search used for a trial count because p is not an integer. More precisely, a calculator table can use decimal increments and help bracket p, but an integer-step table is unsuitable and does not supply the requested numerical root. Use an intersection or zero calculation for the final solution with $0\le p\le1$.