Problem

The table below cross classifies the price of 490 stocks in a particular stock exchange, with whether the earnings per share ratio was positive or not. Use the data in the table to find the probability that the price of the stock is $\$ 50.00$ - $\$ 99.99$ or the earnings per share ratio is positive.
\begin{tabular}{|l|c|c|}
\hline & \multicolumn{2}{|c|}{ Earnings per Share } \\
\hline Price of Stock & Negative or $\mathbf{0}$ & Positive \\
\hline$\$ 0-\$ 49.99$ & 21 & 128 \\
\hline$\$ 50.00-\$ 99.99$ & 16 & 184 \\
\hline$\$ 100.00$ or higher & 2 & 139 \\
\hline
\end{tabular}

Set-up an equation to find the probability of the event occurring. Choose the correct answer below.
A. $P(E)=\frac{184}{490}$
B. $P(E)=\frac{128+16+184+139}{490}$
C. $P(E)=\frac{184}{100}$
D. $P(E)=\frac{16}{128+184+139}$

The probability that the price of the stock is $\$ 50.00$ - $\$ 99.99$ or the earnings per share ratio is positive is $\square$.
(Round to four decimal places as needed.)

Answer

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Answer

Final Answer: The probability that the price of the stock is $50.00 - $99.99 or the earnings per share ratio is positive is \(\boxed{0.9531}\).

Steps

Step 1 :The question is asking for the probability that the price of the stock is between $50.00 and $99.99 or the earnings per share ratio is positive. This is a question of probability, and we can solve it by adding the probabilities of the two events.

Step 2 :The total number of stocks is 490. The number of stocks with a price between $50.00 and $99.99 is 16 + 184 = 200. The number of stocks with a positive earnings per share ratio is 128 + 184 + 139 = 451.

Step 3 :The probability of the price of the stock being between $50.00 and $99.99 or the earnings per share ratio being positive is the sum of the two probabilities, but we need to subtract the probability of the intersection of the two events (i.e., the stocks that have both a price between $50.00 and $99.99 and a positive earnings per share ratio), which is 184/490, to avoid double counting.

Step 4 :So, the equation to find the probability of the event occurring is \((200/490) + (451/490) - (184/490)\).

Step 5 :Calculating this gives us a probability of approximately 0.9531.

Step 6 :Final Answer: The probability that the price of the stock is $50.00 - $99.99 or the earnings per share ratio is positive is \(\boxed{0.9531}\).

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