Question

rashid is playing a game where he selects a card from a deck of four cards, labeled 1, 2, 3, or 4. the possible cards and probabilities are shown in the chart below.

\

$$\begin{array}{|c|c|} \\hline \\text{card} & \\text{probability} \\\\ \\hline 1 & 20\\% \\\\ \\hline 2 & 32\\% \\\\ \\hline 3 & 39\\% \\\\ \\hline 4 & 9\\% \\\\ \\hline \\end{array}$$

what is the expected value for the card that rashid selects?

2.5
2.41
2.45
2.37

Explanation:

Convert percentages to decimals

Using the Percentage to Decimal Conversion knowledge point

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$$

Set up the expected value formula

The expected value \(E(X)\) of a discrete random variable is calculated by summing the products of each possible outcome and its corresponding probability:

$$E(X) = \sum [x \cdot P(X = x)]$$

Calculate the expected value

Substitute the values and compute the sum:

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$$

Answer:

• 2.5
• 2.41
• 2.45
• 2.37 (Correct answer)