SOLUTION: Nina’s father said, if in one grading period her grade in Probability and Statistics is 90 and above, he will add Php 50 to her daily allowance, Php 20 if her grade is 80-89, but

Question 1178718: Nina’s father said, if in one grading period her grade in Probability and Statistics is 90 and above, he will add Php 50 to her daily allowance, Php 20 if her grade is 80-89, but decrease it by Php10 if her grade is 79 and below. If the probability to get 90 and above is 12%, while she have 45% chance to get 80-89, what is her expected additional allowance for the next quarter?
thank po in advance
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's break down this problem to calculate Nina's expected additional allowance.
**1. Define the Outcomes and Probabilities:**
* **Outcome 1:** Grade 90 and above
* Allowance Increase: Php 50
* Probability: 12% or 0.12
* **Outcome 2:** Grade 80-89
* Allowance Increase: Php 20
* Probability: 45% or 0.45
* **Outcome 3:** Grade 79 and below
* Allowance Decrease: Php 10 (or -Php 10)
* Probability: 1 - (0.12 + 0.45) = 1 - 0.57 = 0.43 (or 43%)
**2. Calculate the Expected Value:**
* The expected value (E) is the sum of each outcome multiplied by its probability.
* E = (Outcome 1 * Probability 1) + (Outcome 2 * Probability 2) + (Outcome 3 * Probability 3)
* E = (50 * 0.12) + (20 * 0.45) + (-10 * 0.43)
* E = 6 + 9 - 4.3
* E = 15 - 4.3
* E = 10.7
**3. Interpret the Result:**
* Nina's expected additional allowance for the next grading period is Php 10.70.
**Therefore, Nina's expected additional allowance is Php 10.70.**

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