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COMEDK202510 May 2025Morning ShiftMathematicsProbabilityActual

Vasant and Jothi play a game with a coin. Vasant stakes ₹1 and throw the coins four times. If he throws four heads, he gets his stake and ₹3 from Jothi. If he throws only three heads and they are consecutive, he gets his stake and ₹ 2 from Jothi. If he throws only two heads and they are consecutive, he gets his stake and ₹1 from Jothi. In all other cases Jothi takes the stake money. Find the expectation of Vasant's g

Options

  1. A1
  2. B- 5 8
  3. C5 8
  4. D0

Correct answer

D. 0

Step-by-step solution

The total number of outcomes when tossing a coin four times is 2^4 = 16 . Let X be the gain of Vasant. The possible outcomes are: 1. Four heads: HHHH. This occurs in 1 case. Vasant gets his stake back plus ₹3, so gain is +3 . 2. Three consecutive heads: HHHT, THHH. This occurs in 2 cases. Vasant gets his stake back plus ₹2, so gain is +2 . 3. Two consecutive heads: HHTT, THHT, TTHH. Note that HHHH is already counted in case 1, and HHHT/THHH are in case 2. The outcomes with exactly two consecutive heads are HHTT, TH

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