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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?
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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
∴ Number of outcomes when the coin is tossed thrice = `2xx2xx2=8`
Similarly, the number of outcomes when the coin is tossed four times =`2xx2xx2xx2=16`
Similarly, the number of outcomes when the coin is tossed five times =`2xx2xx2xx2xx2=32`
Similarly, the number of outcomes when the coin is tossed 'n' times = `2xx2xx.......n`times `= 2^n`
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