Question:
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
Solution:
Total number of outcomes when a coin is tossed once = 2 (Heads, Tails)
Number of outcomes when the coin is tossed for the second time = 2
$\therefore$ Number of outcomes when the coin is tossed thrice $=2 \times 2 \times 2=8$
Similarly, the number of outcomes when the coin is tossed four times $=2 \times 2 \times 2 \times 2=16$
Similarly, the number of outcomes when the coin is tossed five times $=2 \times 2 \times 2 \times 2 \times 2=32$
Similarly, the number of outcomes when the coin is tossed ' $n$ ' times $=2 \times 2 \times \ldots . n$ times $=2^{n}$