A child is playing a game of connect-four. The playing board is a 4 × 4 grid. The child is playing with different colored pieces: there are red, blue and green pieces. For each possible spot in the grid, she decides to put either a red, blue or green piece. Each color has exactly a 1/3 chance of being placed in any one square. The choices are independent from spot to spot. • What is the probability that the first row contains at least one green piece? • Given that the first row contains no green pieces, what is the chance that it is all red? • Given that there are no green pieces on the board, what is the probability that there are at least two adjacent squares (vertically or horizontally) with the same color?
A child is playing a game of connect-four. The playing board is a 4 × 4 grid. The child
is playing with different colored pieces: there are red, blue and green pieces. For each possible spot in the
grid, she decides to put either a red, blue or green piece. Each color has exactly a 1/3 chance of being
placed in any one square. The choices are independent from spot to spot.
• What is the probability that the first row contains at least one green piece?
• Given that the first row contains no green pieces, what is the chance that it is all red?
• Given that there are no green pieces on the board, what is the probability that there are at least two
adjacent squares (vertically or horizontally) with the same color?
• What is the expected number of “four of a kind”? (Either as a column, a row, or diagonally).
• What is the expected number of blue pieces on the board?
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