I was wondering if someone could help me with this...
A fair coin is tossed repeatedly, with successive independent tosses, until two consecutive heads OR two consecutive tails are observed. X is the number of tosses required to achieve this.
Explain why the probability mass function of X is given by:
P(X=n) = (1/2)^(n-1) where n=2,3,4,....
Thank you to all x
You should try and see a pattern for the general case of n tosses by calculating the probability for n = 2, 3, 4, .....
Originally Posted by onemoretime29
n = 2: Require HH or TT. Pr(n = 2) = (1/2)^2 + (1/2)^2 = 1/2.
n = 3: ....
n = 4: ....