Kevin is doing an experiment where he flips a fair coin 20 times and analyzes the results. the coin has come up heads the first 19 trials. what is the conditional probability that the next flip will come up tails, given that the previous 19 flips were heads?

P(tails | previous 19 flips were heads) =P(tails I previous 19 flips being heads)/P(previous 19 flips being heads) Since the events are independent (one coin flip does not effect the result of another coin flip), the P(tails I previous 19 flips were heads)=P(tails)*P(previous 19 flips were heads). Thus, the P(previous 19 flips were heads) cancels out, giving us P(tails | previous 19 flips were heads)=P(tails)=1/2. Thinking an outcome is more likely to happen is a common fallacy. It may be highly unlikely to see 20 heads flipped in a row, but the hard part has already been accomplished (the 19 heads being flipped in a row).

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

hope this !

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