players in a card game use the spinner below to determine how many cards they will pick up during their…
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
Answer
Explanation:
Step1: Recall expected - value formula
The formula for the expected value $E(X)$ of a discrete - random variable is $E(X)=\sum_{i}x_{i}P(x_{i})$, where $x_{i}$ are the possible values of the random variable and $P(x_{i})$ are their corresponding probabilities.
Step2: Calculate the product for each value
For $x_1 = 1$ and $P(x_1)=0.5$, the product is $1\times0.5 = 0.5$. For $x_2 = 2$ and $P(x_2)=0.3$, the product is $2\times0.3=0.6$. For $x_3 = 3$ and $P(x_3)=0.2$, the product is $3\times0.2 = 0.6$.
Step3: Sum up the products
$E(X)=0.5 + 0.6+0.6=1.7$.
Answer:
$1.7$