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Directions: Read and Analyze the Problem. Complete the table by supplying the data in each number. Problem number 1:
The SK Officials of Barangay Minamahal decided to conduct a lottery for the benefit of less privileged individuals of their Barangay Two hundred tickets will be sold. One Ticket will win Php 5,000, Five tickets will win Php 3,000, Eight tickets will win Php 1,000, Ten Tickets will win Php 500 and the other tickets will win nothing. if you will buy one ticket, what will be your Expected and Variance gain?​

Sagot :

HELPERNJ

Answer:

So, your expected gain is Php 165, and your Variance Gain is Php 27,095.03 if you buy one ticket

Step-by-step explanation:

To find the Expected Gain, we need to multiply each prize amount by the probability of winning that prize, and then sum up all the products.

Let's calculate the Expected Gain:

E(x) = (1/200) * 5000 + (5/200) * 3000 + (8/200) * 1000 + (10/200) * 500

E(x) = 25 + 75 + 40 + 25

E(x) = 165

So, if you buy one ticket, your expected gain is Php 165.

Next, to find the Variance Gain, we need to calculate the squared difference between each prize amount and the expected gain, multiply it by the probability of winning that prize, and then sum up all the products.

Let's calculate the Variance Gain:

V(x) = [(5000 - 165)^2 * (1/200)] + [(3000 - 165)^2 * (5/200)] + [(1000 - 165)^2 * (8/200)] + [(500 - 165)^2 * (10/200)]

V(x) = [4835^2 * (1/200)] + [2835^2 * (5/200)] + [835^2 * (8/200)] + [335^2 * (10/200)]

V(x) = [23337422.5] + [3368662.5] + [58587.5] + [28058.75]

V(x) = 27095030.75

Therefore, the Variance Gain is Php 27,095.03.

So, your expected gain is Php 165, and your Variance Gain is Php 27,095.03 if you buy one ticket

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