Question

Flip a coin three times. You will win $2 for each heads. What is the expected winning (expectation of your winning)

Answer 1

The three coins could land any these 8 ways:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

P(3 heads) = 1 way out of 8  or 1/8

P(2 heads) = 3 ways out of 8 or 3/8

P(1 head) = 3 ways out of 8 or 3/8

P(0 heads) = 1 way out of 8 or 1/8

x=Winnings  P(x)  E(x)=x�P(x)

    $3      1/8      $.375

    $2      3/8      $.75

    $1      3/8      $.375

  -$10      1/8     -$1.25

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Total expectation =   $ .25