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Hot stock price $=1000$

Gain each day$=30\%$

Loss each day$=25\%$

Probability$=0.5$

Find the worth of the stock after the first day:

Gain: $\$1000+\$1000脳30\%=\$1300$

Loss:localid="1649856969788" $\$1000-\$1000脳25\%=\$750$

Find the worth of the stock after the second day:

2 Gains:$\$1300+\$1300脳30\%=\$1690$

Gain+Loss (or Loss+Gain): $\$1300-\$1300脳\$25\%=\$975$

2 Losses: $\$750-\$750脳25\%=\$562.50$

The probability of each outcome is equal (note: first a gain and then a loss is the same as obtaining first a loss and then a gain):

localid="1649856974109" $$\begin{gathered} P(\$1690)=\left(\frac{1}{4}\right) \\ =0.25 \\ P(\$975)=\left(\frac{2}{4}\right) \\ =\$0.5 \\ P(\$562.50)=\left(\frac{1}{4}\right) \\ =0.15\$ \end{gathered}$$

Hot stock price$=1000$

Gain each day$=30\%$

Loss each day$=25\%$

Probability$=0.5$

Find the worth of the stock after the first day:

Gain: $\$1000+\$1000脳30\%=\$1300$

Loss: $\$1000-\$1000脳25\%=\$750$

Find the worth of the stock after the second day:

2 Gains: $\$1300+\$1300脳30\%=\$1690$

Gain+Loss (or Loss+Gain): $\$1300-\$1300脳25\%=\$975$

2 Losses: $\$750-\$750脳25\%=\$562.50$

It is equally likely that you will obtain either a gain or a loss (note: obtaining a gain followed by a loss is the same as obtaining a loss followed by a gain):

localid="1649856982682" $$\begin{gathered} P\left(\mathrm{\$}1690\right)=\frac{1}{4} \\ =0.25 \\ P\left(\mathrm{\$}975\right)=\frac{2}{4} \\ =0.5 \\ P\left(\mathrm{\$}562.50\right)=\frac{1}{4} \\ =0.25 \end{gathered}$$

Each possibility is multiplied by its probability to arrive at the expected value:

$$\begin{gathered} 渭=鈭�xP\left(x\right) \\ =\mathrm{\$}1690脳0.25+\mathrm{\$}975脳0.5+\mathrm{\$}562.50脳0.25 \\ =\mathrm{\$}1050.625 \end{gathered}$$