# Return to the closing stock prices per share for eight recently traded stocks from a portfolio

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## Instruction Details

1. Return to the closing stock prices per share for eight recently traded stocks from a portfolio, with five closing higher and the others did not.  What is the probability a randomly selected stock from this portfolio did not close higher in recent trading?  Again, express the answer as a fraction, written horizontally: #/#

2. Now express this complementary probability for the chance a stock did not close higher as a percentage, without rounding but include the percent symbol.

3. Notice what happens when you add the complementary fractions together?  What happens when you add the complementary percentages together?  What amount do you get?  The total or the whole, yes!?

Agree or disagree?

4. When you added the two complementary fractions in the closing stock prices examples, you get … one or 1, agreed?

5. When you add the complementary percentages together, what percentage do you get?  Report it with the percent symbol without any insignificant digits.

6. A probability is compound if it considers at least two events or outcomes at the same time.

Returning to the closing stock prices example, if five stocks closed higher and one stock closed unchanged in the portfolio of eight stocks after recent trading, what is the probability that the stock closed either higher or unchanged?  That would be a compound event, selecting a stock that closed either higher or unchanged.  Agreed?

7. Now, continuing with this example with closing stock prices example when five stocks closed higher and one stock closed unchanged in the portfolio of eight stocks after recent trading, determine that probability for randomly selecting a stock that closed either higher or unchanged after recent trading.  Express the answer as a percentage, including percent symbol but without insignificant digits.

8. How did you compute the previous answer for the probability of randomly selecting a stock from a portfolio that either closed higher or closed unchanged after recent trading?  What did you do with the individual or simple probabilities for stocks that closed higher and stocks that closed unchanged?  Describe your arithmetic operation in a single, three-letter word.  Two words could work that are associated with an arithmetic operation that is not subtraction, multiplication or division.  Now you got it?  Report only one of the two words, your choice, all lower case letters.  You got this!

9. Therefore, continuing with this example with closing stock prices example when five stocks closed higher and one stock closed unchanged in the portfolio of eight stocks after recent trading, determine that probability for randomly selecting a stock that closed neither higher nor unchanged after recent trading.  Express the answer as a percentage, including percent symbol but without insignificant digits.

10. As a reminder, when you add together the probability of an either or event along with the probability of its corresponding neither nor event, you get 100%.

Agree or disagree?

### 1. Probability of Not Closing Higher

I agree that the probability of randomly selecting a stock from the portfolio that did not close higher can be calculated by dividing the number of stocks that did not experience a higher closing (2) by the total number of stocks in the portfolio (8). Mathematically, this gives us a probability of 2/8. This fraction represents the likelihood that a randomly chosen stock did not perform better in recent trading.

### 2. Complementary Probability as Percentage

I concur that expressing the complementary probability of a stock not closing higher as a percentage involves multiplying the fraction (2/8) by 100. This results in a percentage of 25%. This percentage gives a clear perspective on the portion of the portfolio that didn’t see higher closing prices in recent trades.

I agree that the concept of adding complementary probabilities is intriguing. Combining the probability of a stock not closing higher (25%) with the probability of a stock closing higher (75%) yields a sum of 100%, which essentially encompasses all possible outcomes for the given scenario. This makes intuitive sense, as when you consider all the possibilities, they should collectively add up to the entire range of potential outcomes.

### 4. Understanding Total Probabilities

I agree that when we add the probabilities of an event and its complementary event, the sum invariably equals 100%. This principle is evident in the example discussed, where the probabilities of stocks either not closing higher (25%) or closing higher (75%) sum up to a comprehensive total of 100%. This serves as a fundamental concept in probability theory, reflecting the exhaustive coverage of all possible outcomes in a given situation.

### 5. Compound Probability with Higher or Unchanged Stock Prices

Agreed. When considering the probability of a stock closing either higher or unchanged, it involves a compound event because it encompasses two distinct outcomes simultaneously.

### 6. Probability of Selecting Higher or Unchanged Stock

The probability of randomly selecting a stock that closed either higher or unchanged after recent trading can be determined by adding the individual probabilities of stocks that closed higher (5/8) and the one stock that closed unchanged (1/8). So, the probability is (5/8) + (1/8) = 6/8. To express this as a percentage, we get 6/8 * 100% = 75%.

### 7. Arithmetic Operation for Calculating Probability

The arithmetic operation used to compute the probability of randomly selecting a stock that closed either higher or unchanged is addition.

### 8. Probability of Selecting Neither Higher nor Unchanged Stock

To find the probability of randomly selecting a stock that closed neither higher nor unchanged, we must consider the complementary event. This means we subtract the probability of selecting a stock that closed either higher or unchanged (6/8 or 75%) from 100% because, as previously mentioned, when you add together the probability of an “either-or” event with its corresponding “neither-nor” event, you get 100%. Therefore, the probability of selecting a stock that closed neither higher nor unchanged is 100% – 75% = 25%.

### 9. Agree

I agree. When you add together the probability of an “either-or” event along with the probability of its corresponding “neither-nor” event, the sum always equals 100%. This fundamental principle reflects the exhaustive coverage of all possible outcomes in a given situation.