(a) A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there?
(b) How many possible outcomes if the coin is tossed:
(i) four times? (ii) five times? (iii) n times?

Answer

(a) 8 (b) (i) 16 (ii) 32 (iii) `2^(n)`

Explanation

(a) In a single throw of a coin there are 2 possible outcomes namely Head (H) and Tail (T).
So, by the fundamental principle of multiplication, the total number of possible outcomes in 3 tosses `=(2xx2xx2)=2^(3)=8.`
(b) Similarly, we have
(i) total number of possible outcomes in 4 losses `=(2xx2xx2xx2)=2^(4)=16.`
(ii) total number of possible outcomes in 5 losses `=(2xx2xx2xx2xx2)=2^(5)=32.`
(iii) total number of possible outcomes in n tosses `=2^(n).`