Answer:
a. Probability of Event A = 2.724037476607E−24
b. G19 = 0.123
c. P(Winning) = 0.475
Step-by-step explanation:
Given
Red (r) = 19
Green (g) = 19
Black (b) = 2
Total = 19 + 19 + 2 = 40
a. In 40 spins of the wheel, find the probability of event A = {19 reds, 19 greens, and 2 blacks}.
This is calculated as follows;
Let P(R) = Probability of Red
P(R) = 19/40
Let P(G) = Probability of Green
P(G) = 19/40
Let P(B) = Probability of Black
P(B) = 2/40
Total number of arrangement = 40!/(19!19!2!) = 27,569,305,764,000
Probability of Event A = 27,569,305,764,000 * (19/40)^19 * (19/40)^19 * (2/40)^19
Probability of Event A = 2.724037476607E−24
b. In 40 spins of the wheel, find the probability of the event G19 = {19 greens}.
Let P(G) = Probability of Green
P(G) = 19/40
Let P(Other) = Probability of any colour other than green = (2+19)/40
P(Other) = 21/40
Total = 40C19
G19 = 40C19 * (19/40)^19 * (21/40)^21
G19 = 0.125525075056335
G19 = 0.123 ---- Approximated
c. Given that you randomly choose to bet red and green only, what is the probability p that you bet a winner?
Let P(R) = Probability of Betting Red
P(R) = 19/40
Let P(G) = Probability of Betting Green
P(G) = 19/40
Let P(Winning) = Probability of Winning
P(Winning) = ½ * P(G) + ½ * P(R)
P(Winning) = ½ * 19/40 + ½ * 19/40
P(Winning) = ½(19/40 + 19/40)
P(Winning) = ½(38/40)
P(Winning) = 19/40
P(Winning) = 0.475
