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15 January, 12:43

Assume a person pays $1 to play the following game. Four coins are tossed. If all coins show the same (all heads or all tails), the player wins $6; otherwise, the player loses. Find the expected value for this game.

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  1. 15 January, 14:38
    0
    For each toss the probability is 0.5 head and 0.5 tail.

    As you have 4 coins you have 0.5 probability for head in each coin also about the tails.

    The probability of all heads is 0.5^4 and all tails is 0.5^4 so the probability of win is 0.5^4+0.5^4=0.125

    The expected value is $6*0.125 - $1 * (1-0.125) = - 0.125$

    (1-0.125) is the propability of fail.

    -$1 is the money that you would lose
  2. 15 January, 15:35
    0
    I believe that answer shall be 24
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