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A source generates three symbols with probabilities $0.25,0.25,0.50$ at a rate of $3000$ symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate as

1. $6000 \; \mathrm{bits} / \mathrm{sec}$
2. $4500 \; \mathrm{bits} / \mathrm{sec}$
3. $3000 \; \mathrm{bits} / \mathrm{sec}$
4. $1500 \; \mathrm{bits} / \mathrm{sec}$