# Probability problem

• Oct 12th 2008, 10:13 AM
onemoretime29
Probability problem
Hey.

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
• Oct 12th 2008, 12:57 PM
mr fantastic
Quote:

Originally Posted by onemoretime29
Hey.

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, .....

n = 2: Require HH or TT. Pr(n = 2) = (1/2)^2 + (1/2)^2 = 1/2.

n = 3: ....

n = 4: ....

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