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COMEDK · Maths · 36. Probability

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 gain.

  1. A \(1\)
  2. B \(-\dfrac{5}{8}\)
  3. C \(\dfrac{5}{8}\)
  4. D \(0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(0\)

Step-by-step Solution

Detailed explanation

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.…