Bulbs are packed in a cartoon each containing 40 bulbs. 700 cartoons were examined for defective bulbs and results are given in the table.
No. of defective bulbs              Frequency
0                                                400
1                                                 180
2                                                  48
3                                                  41
4                                                   18
5                                                    8
6                                                    3
more than 6                                    2
One cartoon is selected at random. What is the probability that it has:
a)no defective bulbs.
b)defective bulbs from 2 to 6.
c)defectve bulbs less than 4.

number of defective bulbs 0 1 2 3 4 5 6 more than 6
frequency 400 180 48 41 18 8 3 2
 


a.Number of non-defective bulbs = 400Number of favourable outcomes = 400Total number of bulbs = 700Total number of possible outcomes = 700Pno defective bulb = Number of favourable outcomes Total number of possible outcomes = 400700 = 47b.Number of 2 defective bulbs = 48Number of 3 defective bulbs = 41Number of 4 defective bulbs = 18Number of 5 defective bulbs = 8Number of 6 defective bulbs = 3Number of favorable outcomes = 48 + 41 + 18 + 8 + 3 = 118Pdefective bulbs 2 to 6 =Number of favorable outcomesTotal number of possible outcomes = 118700 = 59350c.Number of 0 defective bulbs = 400Number of 1 defective bulbs = 180Number of 2 defective bulbs = 48Number of 3 defective bulbs = 41Number of favourable outcomes = 400 + 180 + 48 + 41 = 669Pdefective bulbs less than 4 = Number of favorable outcomesTotal number of possible outcomes = 669700

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a)-no. of box having no defective bulbs n(E)=400
total no. of boxes n(S)=700
P(E)=n(E)/n(S)=400/700=4/7
b)-no. of box having defective bulbs from 2 to6=118
P(E)=n(E)/n(S)=118/700=59/350
c)-no. of boxes having less than4 defective bulbs=669
P(E)=n(E)/n(S)=669/700
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