In a coffee shop "Scratch and Win" contest, one out of three cards is a winner. What is the probability that Shenice would first win on her third try?

a. 4/9

b. 1/27

c. 4/27

d. 8/81

Answer: C.) 4/27

Step-by-step explanation:

Given that:

One out of three cards is a winner:

P (winning) = 1 / 3

Therefore, P (not winning) = P (losing):

1 - P (winning) = 1 - 1/3 = 2/3

Probability that shenice will first win on her third try can be interpreted as:

1st try = lose, 2nd try: lose, 3rd try : win

P (losing) * p (losing) * p (winning)

(2/3) * (2/3) * (1/3)

4 / 27

Probability of first winning on third try = 4/27