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Question

Bulbs are packed in cartons each containing 40 bulbs. sevenhundred cartons were examined for defective bulbs and the results are in the following table: number of defective bulbs in a carton 0,1,2,3,4,5,6andmorethan6 , frequency 400180484118832 one carton was selected at random. what is the probability that it has (i) no defective bulb? (ii) defective bulbs from 2to6? (iii) defective bulbs less than4?


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Solution

Number of defective bulbs in cartonFrequency
0400
1180
248
341
418
58
63
More than 62

The total number of bulbs (N)=400+180+48+41+18+8+3+2=700

(I)

Let E be the event that it has no defective bulbs

Total number of bulbs = 700

The number of favourable outcomes to E= 400

Therefore, P(E)=400700=47

(II) Let F be the event that it has 2to6 defective bulbs.

Total number of bulbs =700

The number of favourable outcomes to F=48+41+18+8+3=118

Therefore, P(F)=118700=59350

(III) Let G be the event that it has less than four defective bulbs.

Total number of bulbs =700

The number of favourable outcomes to G=400+180+41=669

Therefore, P(G)=669700


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