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You roll a standard die. You win $12 if you roll a six, $6 if you roll a one, and $0 if you roll anything else. What is the expected value of a single roll?
$3
$2
$9
$18​

Answer :

Fichohgo

The expected value from a single die roll Given the Conditions stated is $3

The expected value is calculated using the relation :

  • E(X) = X × P(X)

The table of probabilities from a single roll :

  • X ___ 6 ___ 0 ___ 0 ___ 0 ___ 0 ___12
  • P(X)_ 1/6__ 1/6 __ 1/6 __ 1/6 __ 1/6 __ 1/6

The expected value calculation :

  • E(X) = X × P(X)

  • E(X) = (6×1/6) + 0 + 0 + 0 + 0 + (12 × 1/6)

  • E(X) = 1 + 2 = $3

Therefore, the expected value of a single die roll is $3

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