5. A transmitter sends two signals, A and B, corrupted by noise. If the signal-t

Question

5. A transmitter sends two signals, A and B, corrupted by noise. If the signal-to-noise ratio is too low you cannot reliably reconstruct the original signal (bad signal quality). You found that the probability of A to have "good" signal quality is 0.6.The probability of B to have good signal quality is 0.5, and the probability that A has good signal quality given that B has good signal quality is 0.7. Find a. The probability that both signals have good quality b. The probability that signal B has good quality given that signal A has good quality

Explanation / Answer

5 a) P(Both signals have good quality)

= P(A and B good Quality)

= P(Good Quality A | Good Quality B)*P(Good Quality B)

= 0.7*0.5

= 0.35

b) P(Good Quality B| Good Quality A)

= P(Both Good Quality) / P(Good quality A)

= 0.35 / 0.60

= 7/12

= 0.5833 [Rounded off to 4 decimal places]

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