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A roulette wheel has 38 numbers, with 18 odd numbers (black) and 18 even numbers (red),...

A roulette wheel has 38 numbers, with 18 odd numbers (black) and 18 even numbers (red), as well as 0 and 00 (which are green). If you bet $19 that the outcome is an odd number, the probability of losing the $19 is 20/38 and the probability of winning is $38 (for a net gain of only $19, given you already paid $19) is 18/38.

If a player bets $19 that the outcome is an odd number, what is the player's expected value? (The answer is -$1.00). *****Please show the calculation of how they came to the (-$1.00)*****

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Answer #1

Expected value = net gain * P(winning) - net loss * P(loosing)

= (19 * 18/38) - (19 * 20/38)

= -$ 1 (ans)

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