Favorable Outcomes in a Game?
Rahul and Aarav are playing a board game where they can earn rewards based on the roll of a fair six-sided die. Rahul is offered a deal: if the die lands on an even number, he gets a reward of Rs. 20, but if it lands on an odd number, he loses Rs. 15. Aarav, on the other hand, is offered a deal that guarantees him a reward of Rs. 20 if the die lands on an even number, with no loss in case of an odd number. Assuming both deals are equally likely to happen, which one should Rahul prefer, and why?
1 Answer
📌 CONCEPT: Probability is a measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
📐 RULE / FORMULA: To calculate the probability of an event, we use the formula P(event) = Favorable Outcomes / Total Outcomes.
💡 WORKED EXAMPLE: In this case, Rahul wins Rs. 20 if the die lands on an even number (2, 4, or 6). The probability of an even number being rolled is P(even) = 3/6 = 1/2. Since Rahul also loses Rs. 15 if the die lands on an odd number, we need to calculate the probability of an odd number being rolled, which is P(odd) = 3/6 = 1/2. Now, let's calculate the expected value for Rahul's deal: EV(Rahul) = (P(even) * Rs. 20) - (P(odd) * Rs. 15) = (1/2 * 20) - (1/2 * 15) = Rs. 2.50. Similarly, for Aarav's deal, EV(Aarav) = (P(even) * Rs. 20) = (1/2 * 20) = Rs. 10. Since 10 is greater than 2.50, Rahul should prefer Aarav's deal.
⚠️ COMMON MISTAKE: Students often forget to calculate the expected value, which is essential in such problems involving uncertain outcomes.
10 Jun 26
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