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Q.

(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective? 

(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

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answer is 1.

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Detailed Solution

Given: total number of bulbs = 20 and number of defective bulbs = 4

So not defective = 20 - 4 = 16

(i) getting the defective bulb

We know that, P(E) = (Number of favorable outcomes/ Total number of outcomes)

 P (defective bulb) = 4/20 

= 1/5 = 0.2

(ii) Since 1 non-defective bulb is drawn, then the total number will be 19

So the new total number of events = 19

Number of non-defective bulbs = 19 - 4 = 15

P(not defective bulb) = 15/19 

= 0.789

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