Question

In a popular casino​ game, you can bet one whether a ball will fall in an arc on a wheel colored​ red, black, or green. Say the probability of a red outcome is StartFraction 18/38 EndFraction 18/38​, that of a black outcome is StartFraction 18/ 38 EndFraction 18/38​, and that of a green outcome is StartFraction 2/38 EndFraction 2/38. Suppose someone makes a ​$20 bet on black. Find the expected net winnings for this single bet.

Answer 1

Answer:

The expected net winnings for the bet are -$1.0526

Step-by-step explanation:

P(x =+$20) = P(Black outcome) = 18/38

P(x =-$20) = P(red outcome) + P(green outcome)

= 18/38 + 2/38 = 20/38

Hence the probability distribution of x = $20 , P(x) = 18/38

x = -$20, P(x) = 20/38

Expected value of the random variable x is given by ;

miu = Summation [xP(x)] = 20(18/38) - 20( 20/38)

= -$1.0526

hence, the expected net winnings for the bet are -$1.0526

This implies that if a player bet on a very large number of games, the player would on the average lose $1.0526 per single bet