One game at a carnival is called “Duck Pond.” This game consists of a large number of ducks that are floating through an oval-shaped trough. A sign claims that 20% of the ducks have a blue dot on the bottom of them, 20% have a red dot, 20% have a green dot, 20% have a yellow dot, and 20% have an orange dot. Players pay to select one duck, show the color to the game attendant, replace the duck, spin around once, and then select a second duck. If the dot on the bottom of the second duck matches the dot that was on the bottom of the first duck, the player wins. Otherwise, the player loses. a) Are the events “color of the first duck” and “color of the second duck” independent? Explain.
b) You want to perform a simulation to estimate the probability of winning this game, assuming the duck colors are distributed as claimed. Describe how you could use a table of random digits to carry out this simulation without needing to skip any digits.
c) Perform 10 trials of the simulation described in part (b) using the random digits given. Mark on or below the digits to show your work.
19223 95034 05756 28710 96409 12531 42544 82853 17463 74773 48364 00193 17483 19490
Based upon your simulation, what is the estimated probability of winning this game?