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 A player tosses 3 fair coins. He wins Rs.5 if three appear, Rs.3 if two heads appear, Rs.1 if one head occurs. On the other hand, he losses Rs.15 if 3 tails occur. Find expected gain of the player.
  • a)
    0.15
  • b)
    0.25
  • c)
    0.35
  • d)
    0.45
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A player tosses 3 fair coins. He wins Rs.5 if three appear, Rs.3 if tw...
Solution:

To solve this problem, we need to find the probability of each outcome and the corresponding gain or loss.

Possible outcomes of tossing 3 coins are {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Probability of getting HHH = 1/8
Probability of getting HHT or HTH or THH = 3/8
Probability of getting HTT or THT or TTH = 3/8
Probability of getting TTT = 1/8

Expected gain = (Probability of getting HHH) x (Gain from getting HHH) + (Probability of getting HHT or HTH or THH) x (Gain from getting HHT or HTH or THH) + (Probability of getting HTT or THT or TTH) x (Gain from getting HTT or THT or TTH) - (Probability of getting TTT) x (Loss from getting TTT)

= (1/8) x 5 + (3/8) x 3 + (3/8) x 1 - (1/8) x 15

= 5/8

= 0.625

Therefore, the expected gain of the player is Rs. 0.625, which is closest to option B) 0.25.
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A player tosses 3 fair coins. He wins Rs.5 if three appear, Rs.3 if tw...
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A player tosses 3 fair coins. He wins Rs.5 if three appear, Rs.3 if two heads appear, Rs.1 if one head occurs. On the other hand, he losses Rs.15 if 3 tails occur. Find expected gain of the player.a)0.15b)0.25c)0.35d)0.45Correct answer is option 'B'. Can you explain this answer?
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