COMEDK · Maths · 36. Probability
In a game, a man wins ₹ 1000 if he gets an even number greater than or equal to 4 on a fair dice and loses ₹ 200 for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his expected gain/loss in (₹) is --
- A \(\dfrac{3800}{9}\) loss
- B \(\dfrac{3800}{9}\) gain
- C \(\dfrac{2200}{9}\) gain
- D \(\dfrac{2200}{9}\) loss
Answer & Solution
Correct Answer
(B) \(\dfrac{3800}{9}\) gain
Step-by-step Solution
Detailed explanation
The outcomes on a fair dice are \(\{1, 2, 3, 4, 5, 6\}\). Winning condition: Even number \(\ge 4\), which are \(\{4, 6\}\). Probability of winning \(p = \dfrac{2}{6} = \dfrac{1}{3}\). Losing condition: Any other number, which are \(\{1, 2, 3, 5\}\). Probability of losing…
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