A new battery Voltage may be acceptable (A) or unacceptable (U). Suppose that 90

Question

A new battery Voltage may be acceptable (A) or unacceptable (U). Suppose that 90% of batteries have acceptable voltages. Batteries are independently selected and tested until two acceptable ones have been found. Let Y denote the number of batteries that must be tested List the outcomes corresponding to each of these events: Y=2, Y=3 and Y= 4 Find the Probabilities P(Y=2),p(Y=3 and P(Y=4) Compute P(second battery is U| Y = 4). the probability that the second battery is unacceptable given that 4 batteries are selected

Explanation / Answer

a) Y=2 is a result of 2 consecutive acceptable batteries taken Y=3 is a result of either of 2 events, when one unacceptable battery is chosen on the 1st or 2nd test while one acceptable battery is selected on the last step and another one is tested on the 1st or 2nd step; Y=4 could be done by 3 ways, when 2 unacceptable batteries are chosen during the 3 first tests while two others are acceptable batteries. b) P2 = 0.9*0.9 = 0.81 P3 = 2*0.1*0.9*0.9*0.9 = 0.1458 P4 = 3*0.1*0.1*0.9*0.9 = 0.0243 c) P(2nd is U| 4 tested)= P4* 2/3 = 0.0162 Good luck!

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