Questions: The pointer shown to the right can land on every number, and the respective probability that the pointer can land on is shown in the table below. Compute the expected value for the number on which the pointer lands. The expected value for the number on which the pointer lands is (Type an integer or a decimal.) Outcome Probability 1 1/4 2 1/4 3 1/2

The pointer shown to the right can land on every number, and the respective probability that the pointer can land on is shown in the table below. Compute the expected value for the number on which the pointer lands.

The expected value for the number on which the pointer lands is
(Type an integer or a decimal.)

Outcome Probability
1 1/4
2 1/4
3 1/2

Transcript text: The pointer shown to the right can land on every number, and the respective probability that the pointer can land on is shown in the table below. Compute the expected value for the number on which the pointer lands. The expected value for the number on which the pointer lands is $\square$ (Type an integer or a decimal.) \begin{tabular}{|c|c|} \hline Outcome & Probability \\ \hline 1 & $\frac{1}{4}$ \\ \hline 2 & $\frac{1}{4}$ \\ \hline 3 & $\frac{1}{2}$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Identify the outcomes and their probabilities

The outcomes and their respective probabilities are given in the table:

Outcome 1: Probability = 1/4
Outcome 2: Probability = 1/4
Outcome 3: Probability = 1/2

Step 2: Set up the expected value formula

The expected value $ E(X) $ is calculated using the formula: \[ E(X) = \sum (x_i \cdot P(x_i)) \] where $ x_i $ are the outcomes and $ P(x_i) $ are their respective probabilities.

Step 3: Calculate the expected value

Substitute the given values into the formula: \[ E(X) = (1 \cdot \frac{1}{4}) + (2 \cdot \frac{1}{4}) + (3 \cdot \frac{1}{2}) \] \[ E(X) = \frac{1}{4} + \frac{2}{4} + \frac{3}{2} \] \[ E(X) = \frac{1}{4} + \frac{2}{4} + \frac{6}{4} \] \[ E(X) = \frac{1 + 2 + 6}{4} \] \[ E(X) = \frac{9}{4} \] \[ E(X) = 2.25 \]