# Entropy when having symbols with same probability

I am trying to work out this problem:

Assume that we are transmitting data from a dictionary of 15 symbols. Let the probability of sending one symbol be the same as that of sending any other symbol. Calculate how often we need to fetch a symbol to transmit information at a rate of 5 bits/s.

How can this be found?

• It would be nice if you write also what you may have thought or tried to do. – FELIPE_RIBAS May 7 '14 at 20:02
• I am starting to learn about entropy, all I basically know is the formula of entropy which in this case I think is not applicable since the probabilities are not given – user1930901 May 7 '14 at 20:22
• @user1930901: 15 equally likely symbols means each symbol has a probability of $1/15$. See my answer for a hint. – Matt L. May 7 '14 at 20:23

HINT: Compute the entropy $$H$$ of your source and note that in your case it represents the number of bits required to represent each symbol. Then from
$$\quad H$$ [bits/symbol] $$\times$$ $$x$$ [symbols/second] = $$5$$ [bits/second]
compute $$x$$.