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A local flower shop is selling $1 raffle tickets and is donating all proceeds to the children's hospital. They sold 5,500 tickets and plan to give away 20 flower arrangements valued at $70 and 20 gift certificates valued at $25. Find the expected value of purchasing a raffle ticket.


Round to the nearest cent. Do not round until the final calculation.

Respuesta :

Answer: The expected value of purchasing a raffle ticket would be $0.3449.

Step-by-step explanation:

Since we have given that

Number of tickets = 5500

Number of flower arrangements = 20

Number of gift certificates = 20

So, Probability that wining $70 at flower arrangement = [tex]\dfrac{20}{5500}=\dfrac{1}{275}[/tex]

Probability that wining $25 at gift certificates = [tex]\dfrac{20}{5500}=\dfrac{1}{275}[/tex]

So, Expected value of purchasing a raffle ticket would be

[tex]70\times \dfrac{1}{275}+25\times \dfrac{1}{275}\\\\=0.254+0.0909\\=\$0.3449[/tex]

Hence, the expected value of purchasing a raffle ticket would be $0.3449.

ajeigbeibraheem

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

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