A coin is tossed three times and the outcomes are recorded.

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 $=2^{n}$

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