Value of a call on a drilling outcome stock

Question

An oil company is drilling a well that succeeds with probability $30\%$ . After the result is known the stock will be worth $100 on success and $20 on failure. You hold the right, but not the obligation, to buy a share at $50 the day after the outcome is announced. What is this option worth?

Short answer

$15. You exercise only on success, earning $100-50=50$ dollars with probability $0.3$ ; failure leaves it worthless. So the value is $0.3\cdot50=15$ .

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Lessons behind this question

Conditional Expectation and Variance Revisited
Conditional Probability, Total Probability, and Bayes' Rule
Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating

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