Questions: Question A data analyst has spreadsheets numbered 1,2, databases numbered 1,2,3, and presentations numbered 1,2,3,4 to work on this week. If a single item is picked at random to work on, what is the probability that the item is a database AND has an odd number? - Provide the final answer as a simplified fraction. Provide your answer below:

Question A data analyst has spreadsheets numbered 1,2, databases numbered 1,2,3, and presentations numbered 1,2,3,4 to work on this week. If a single item is picked at random to work on, what is the probability that the item is a database AND has an odd number? - Provide the final answer as a simplified fraction. Provide your answer below:
Transcript text: Question A data analyst has spreadsheets numbered 1,2 , databases numbered $1,2,3$, and presentations numbered $1,2,3,4$ to work on this week. If a single item is picked at random to work on, what is the probability that the item is a database AND has an odd number? - Provide the final answer as a simplified fraction. Provide your answer below: $\square$
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Solution

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Solution Steps

To solve this problem, we need to determine the total number of items and the number of favorable outcomes (databases with an odd number). The probability is then the ratio of favorable outcomes to the total number of items.

  1. Count the total number of items.
  2. Identify the favorable outcomes (databases with odd numbers).
  3. Calculate the probability as the ratio of favorable outcomes to the total number of items.
Step 1: Count the Total Number of Items

The total number of items is the sum of spreadsheets, databases, and presentations: \[ \text{Total items} = 2 + 3 + 4 = 9 \]

Step 2: Identify Favorable Outcomes

The favorable outcomes are the databases with odd numbers. There are 3 databases numbered 1, 2, and 3. The odd-numbered databases are 1 and 3, so there are 2 favorable outcomes.

Step 3: Calculate the Probability

The probability of picking a database with an odd number is the ratio of favorable outcomes to the total number of items: \[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total items}} = \frac{2}{9} \]

Final Answer

The probability that the item is a database and has an odd number is: \[ \boxed{\frac{2}{9}} \]

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