 A student has to decide whether to stop his studies and work for a job paying ₱4,500 a month or continue his studies and after which a job paying ₱8,000 will be offered to him, if he passes his remaining subjects. The probability that he can pass his remaining subjects is 45%. Find the EV if the student decides to continue his studies.

To compute the **Expected Value (EV)** if the student decides to continue studying, we use the formula:

\[
EV = P(\text{Pass}) \cdot \text{Payoff if Pass} + P(\text{Fail}) \cdot \text{Payoff if Fail}
\]

### Information Given:
1. Payoff if Pass = ₱8,000 per month (salary after passing remaining subjects)
2. Payoff if Fail = ₱0 (assumed no salary because they fail to secure the job)
3. Probability of Passing = 0.45 (45%)
4. Probability of Failing = 1 - 0.45 = 0.55 (55%)

### Calculation:
\[
EV = (0.45 \cdot 8,000) + (0.55 \cdot 0)
\]

\[
EV = 3,600 + 0 = 3,600
\]

### Result:
The **Expected Value** if the student decides to continue studying is **₱3,600 per month**.

This means that, on average, the student would earn ₱3,600 per month if they decide to continue studying, considering the probability of passing and failing.

---

### Follow-Up Questions:
1. How does this EV compare to the immediate job option paying ₱4,500 per month?
2. Should the student factor in other variables like tuition or study expenses when deciding?
3. What is the breakeven probability where continuing studies becomes more beneficial than taking the job?
4. How would the EV change if the probability of passing increased or decreased?
5. What are the long-term impacts of choosing a lower immediate salary versus a higher potential salary?

### Tip:
When using **Expected Value** in decision-making, always consider non-financial factors (e.g., career growth, job satisfaction, risks) alongside financial ones.

A student has to decide whether to stop his studies and work for a job paying ₱4,500 a month or continue his studies and after which a job paying ₱8,000 will be offered to him, if he passes his remaining subjects. The probability that he can pass his remaining subjects is 45%. Find the EV if the student decides to continue his studies.

Learn how to calculate the expected value (EV) for a student deciding between immediate work at ₱4,500/month or continuing studies to earn ₱8,000/month with a 45% probability of passing. This problem covers concepts of expected value and probability, ideal for Grades 10-12.

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