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 than$4$?

Answer 1

Number of defective bulbs in carton	Frequency
0	400
1	180
2	48
3	41
4	18
5	8
6	3
More than 6	2

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

(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\left(E\right)=$$\frac{400}{700}=\frac{4}{7}$

(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\left(F\right)=$$\frac{118}{700}=\frac{59}{350}$

(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\left(G\right)=$$\frac{669}{700}$