Problem 9: There is a 15% probability that a certain type of laser diode has eff

Question

Problem 9: There is a 15% probability that a certain type of laser diode has efficiency below 0.3 mW/mA. These didoes perform independently. (a) If 2 diodes are used, find the probability that both have efficiency below 0.3 mW/mA. (keep 4 decimal places) (b) f 2 diodes are used, find the probability that both do not have efficiency below 0.3 mW/mA. (keep 4 decimal places) (b) ) If 3 diodes are used, find the probability that 1st has efficiency below 0.3 mW/mA while other two do not have efficiency below 0.3 mW/mA.(keep 4 decimal places)

Explanation / Answer

a) Probability that both have a efficiency below 0.3 mW / mA

= Probability that first one has lower efficiency * Probability that the second one has lower efficiency

= 0.15*0.15

= 0.0225

Therefore 0.0225 is the required probability here.

b) Probability that both do not have lower efficiency

= 1 - Probability that both have a lower efficiency

= 1 - 0.0225

= 0.9775

Therefore 0.9775 is the required probability here.

c) The required probability here is computed as:

= 0.15*(1 - 0.15)2

= 0.108375

Therefore 0.1084 is the required probability here. (Rounded to 4 decimal places )

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