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To find the expected number of dots on a card drawn from the deck, we can calculate the expected value by multiplying each number of dots by its corresponding probability and then summing these products. The formula to compute the expected value \( E[X] \) is given by:

\[
E[X] = \sum (x \times P(x))
\]

Where \( x \) is the number of dots on the card and \( P(x) \) is the probability of drawing a card with \( x \) dots. According to the information provided:

- Probability of drawing a card with 1 dot = 0.3
- Probability of drawing a card with 2 dots = 0.1
- Probability of drawing a card with 3 dots = 0.2
- Probability of drawing a card with 4 dots = 0.4

We calculate the expected value as follows:

\[
E[X] = (1 \times 0.3) + (2 \times 0.1) + (3 \times 0.2) + (4 \times 0.4)
\]

Let's compute this.The expected number of dots on a card drawn from this deck is 2.7. Therefore, the correct answer is (D) 2.7.

If you have any further questions or need more details, feel free to ask. Here are some related topics you might find interesting:

1. How to calculate the variance of the number of dots on a card drawn from this deck?
2. What is the probability distribution function and how is it related to this problem?
3. How does changing the probabilities affect the expected value?
4. What would be the expected number of dots if each card was equally likely to be drawn?
5. How does the concept of expected value apply to real-life scenarios?

**Tip:** When dealing with expected values in probability, it's important to ensure that the sum of probabilities equals 1, as it represents the total possible outcomes of the experiment.

A deck contains cards labeled with one, two, three, or four dots. A random card from this deck is drawn. The probabilities of each outcome are as follows: 1 dot - 0.3, 2 dots - 0.1, 3 dots - 0.2, and 4 dots - 0.4. What is the expected number of dots on the card?

Learn how to calculate the expected number of dots on a card drawn from a deck with different probabilities. This problem covers key probability concepts and the expected value formula, suitable for Grades 9-12.

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