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 formula for the expected value $E(X)$ of a discrete random variable is $E(X)=\sum_{i}x_ip_i$, where $x_i$ are the possible values and $p_i$ are their corresponding probabilities.

Step2: Calculate the product for each value - probability pair

For $x_1 = 1$ and $p_1=0.5$, the product is $1\times0.5 = 0.5$.
For $x_2 = 2$ and $p_2 = 0.3$, the product is $2\times0.3=0.6$.
For $x_3 = 3$ and $p_3 = 0.2$, the product is $3\times0.2 = 0.6$.

Step3: Sum up the products

$E(X)=0.5 + 0.6+0.6$.
$E(X)=1.7$.

Answer:

$1.7$