Question

drew 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. what is the expected value for the card that drew selects? 2.3 2.5 2.6 2.2

Explanation:

Step1: Convert percentages to decimals

$22\% = 0.22$, $29\%=0.29$, $26\% = 0.26$, $23\%=0.23$

Step2: Use the expected - value formula $E(X)=\sum_{i}x_ip_i$

$$\begin{align*} E(X)&=(1\times0.22)+(2\times0.29)+(3\times0.26)+(4\times0.23)\\ &=0.22 + 0.58+0.78 + 0.92\\ &=2.5 \end{align*}$$

Answer:

2.5