CONDITIONAL PROBABILITY PRACTICE Given is board of 17 squares. All white squares are labeled as A, while all gray squares are labeled as G as shown below. 1. A pawn is placed in the middle square and a fair coin is thrown three times. If the coin shows heads, the pawn is moved one square to the right, and when the coin shows tails, the pawn is moved one square to the left. A A G A G A A Given are the following two events: A = {the pawn is on a square labeled as A after the third throw} G={the pawn is on a square labeled as G after the third throw} Which event has a greater probability to occur? Why? 2. Which of the squares is the pawn most likely to be after the third throw? A1 A2 G1 A3 G2 A4 A5 3. The fair coin is substituted by a biased coin such that it is twice as likely to show heads. Answer the questions from problems 1 and 2 in regards to the biased coin. 4. What kind of a biased coin should we have in order for the two events (A and G) to be equally likely to occur?