A text is made up of the characters $\alpha, \beta, \gamma, \delta$ and $\sigma$ with the probability $0.12, 0.40, 0.15, 0.08$ and $0.25$ respectively. The optimal coding technique will have the average length of
Answer : B
Alpha=.12 Beta=.40 Gamma=.15 Delta=.08 Sigma=.25 (All are given in question)
Path length with 4= Alpha, Delta. (.48+.32)
Path length with 3= gamma.(.45).
Path length with 2=sigma..(.50).
Path length with 1= beta(.40).
Average path length=2.15 .
We arrange the characters in ascending order according to its Probabilities
So the path length of α=4, β=1,γ=3,δ=4 and σ=2
The optimal path length =(4x0.12)+(1x0.40)+(3x0.15)+(4x0.08)+(2x0.25)
hence ans is B