Question

players in a card game use the spinner below to determine how many cards they will pick up during their turn. the table below shows the probability distribution for the number of cards a player will pick up during one turn. what is the expected value for the number of cards a player will pick up during one turn?

number of cards | probability
--- | ---
1 | 0.5
2 | 0.3
3 | 0.2

Explanation:

Step1: Recall expected value formula

The expected value \( E(X) \) of a discrete random variable is calculated as \( E(X)=\sum x_iP(x_i) \), where \( x_i \) are the values of the random variable and \( P(x_i) \) are their corresponding probabilities.

Step2: Multiply each number of cards by its probability

For \( x = 1 \), \( P(1)=0.5 \), so \( 1\times0.5 = 0.5 \).
For \( x = 2 \), \( P(2)=0.3 \), so \( 2\times0.3 = 0.6 \).
For \( x = 3 \), \( P(3)=0.2 \), so \( 3\times0.2 = 0.6 \).

Step3: Sum the products

Add the results: \( 0.5 + 0.6 + 0.6 = 1.7 \).

Answer:

1.7