Respuesta :
Answer:
[tex] E(X)= 70*\frac{20}{5500} + 25*\frac{20}{5500} -1 \frac{5460}{5500}=-0.647[/tex]
And that represent the expected value of purchasing a raffle ticket.
Step-by-step explanation:
In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".
In order to calculate the expected value we can use the following formula:
[tex]E(X)=\sum_{i=1}^n X_i P(X_i)[/tex]
We need to find the probability for each event. The probability of win a flower arrangement is 20/5500 and a gift crtificate is 20/5500 so then the probability of no win anything is (5500-20-20)/5500= 5460/5500
Then the random variable is given by:
X | 70 | 25 | -1 |
P(X) | 20/5500 | 20/5500 | 5460/5500 |
And thn if we replace we got:
[tex] E(X)= 70*\frac{20}{5500} + 25*\frac{20}{5500} -1 \frac{5460}{5500}=-0.647[/tex]
And that represent the expected value of purchasing a raffle ticket.
The expected value of purchasing a raffle ticket is -0.647.
What is the Expected Value of a Probability & Statistical Analysis?
The expected value is derived in probability analysis by the multiplication of each of the potential possibilities by the likelihood that each result will occur and then adding all of those values together.
Using the formula below, we can calculate the expected value as follows:
[tex]\mathbf{ E(X)= \sum^{n}_{i=1}X_i P(X_i)}[/tex]
However, the probability (Pr)of each event can be categorized as follows:
- Pr (to win a flower arrangement ) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]
- Pr (to gift a certificate) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]
- Pr (no win) ) [tex]\mathbf{=\dfrac{5500 - 20 - 20}{5500}=\dfrac{5460}{5500}}[/tex]
Thus;
[tex]\mathbf{E(X) = 70(\dfrac{20}{5500} \times 25 ((\dfrac{20}{5500} )- 1(\dfrac{5460}{5500} )}[/tex]
[tex]\mathbf{E(X) =-0.647}[/tex]
Learn more about finding the expected value of a probability here:
https://brainly.com/question/9931880
