Problem

The table below cross classifies the price of 498 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 \multicolumn{1}{|c|}{ Price of Stock } & Negative or 0 & Positive \\
\hline$\$ 0-\$ 49.99$ & 24 & 127 \\
\hline$\$ 50.00-\$ 99.99$ & 14 & 190 \\
\hline$\$ 100.00$ or higher & 3 & 140 \\
\hline
\end{tabular}

Set-up an equation to find the probability of the event occurring. Choose the correct answer below.
A. $P(E)=\frac{14}{127+190+140}$
B. $P(E)=\frac{127+14+190+140}{498}$
c. $P(E)=\frac{190}{100}$
D. $P(E)=\frac{190}{498}$

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 approximately 0.946. Therefore, the correct answer is not listed in the options provided. The closest option is B. \(P(E)=\frac{127+14+190+140}{498}\), but this does not account for the double counting of stocks that fall into both categories. \(\boxed{0.946}\)

Steps

Step 1 :The question is asking for the probability that the price of the stock is \(\$50.00 - \$99.99\) or the earnings per share ratio is positive. This means we need to find the total number of stocks that fall into either of these categories and divide by the total number of stocks.

Step 2 :The total number of stocks with a price of \(\$50.00 - \$99.99\) is 14 (negative or 0 earnings per share) + 190 (positive earnings per share) = 204.

Step 3 :The total number of stocks with a positive earnings per share ratio is 127 (price \(\$0 - \$49.99\)) + 190 (price \(\$50.00 - \$99.99\)) + 140 (price \(\$100.00\) or higher) = 457.

Step 4 :However, since we are looking for the probability that the stock falls into either of these categories, we need to make sure we don't double count the stocks that fall into both categories (i.e., stocks with a price of \(\$50.00 - \$99.99\) and a positive earnings per share ratio). These stocks are already included in both of the counts above, so we need to subtract them once to get the correct total.

Step 5 :So, the total number of stocks that fall into either category is 204 (price \(\$50.00 - \$99.99\)) + 457 (positive earnings per share) - 190 (double counted) = 471.

Step 6 :The total number of stocks is 498, so the probability of a stock falling into either category is \(\frac{471}{498}\).

Step 7 :Final Answer: The probability that the price of the stock is \(\$50.00 - \$99.99\) or the earnings per share ratio is positive is approximately 0.946. Therefore, the correct answer is not listed in the options provided. The closest option is B. \(P(E)=\frac{127+14+190+140}{498}\), but this does not account for the double counting of stocks that fall into both categories. \(\boxed{0.946}\)

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