Entropy is a concept borrowed from thermodynamics and information theory. In communication, it measures the degree of uncertainty or unpredictability in a message system. The greater the number of possible messages a source could send, the higher the entropy — because the receiver cannot predict with confidence what will arrive next. Consider a coin toss (low entropy, only two outcomes) versus selecting one square on a 64-square chessboard (high entropy, 64 possible outcomes). High entropy means more information value per message received, because the message resolves greater uncertainty. However, very high entropy also makes communication more difficult because there is little predictability to guide decoding. This is why communication systems balance entropy with redundancy — repeating or reinforcing elements that the receiver can use to reconstruct meaning even under noisy conditions.

The diagonal of the rectangle is 10 and one side is 6.

Using the Pythagorean theorem: $\text{diagonal}^2 = \text{length}^2 + \text{width}^2$

$10^2 = 6^2 + w^2 \Rightarrow 100 = 36 + w^2 \Rightarrow w^2 = 64 \Rightarrow w = 8$

Perimeter $= 2(6 + 8) = 2 \times 14 = 28$.

This is a binomial experiment: $n=10$, $p=P(\text{green})=\dfrac{15}{25}=\dfrac{3}{5}$, $q=\dfrac{2}{5}$.

$\text{Variance} = npq = 10 \times \dfrac{3}{5} \times \dfrac{2}{5} = 10 \times \dfrac{6}{25} = \dfrac{60}{25} = \dfrac{12}{5}$