Question

Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the following table :
`{:("Number of defective bulbs"," 0 1 2 3 4 5 6 More than 6"),("Frequency","400 180 48 41 18 8 3" " 2"):}`
One carton was selected at random. What is the probaility that it has
(i) no defective bulbs ?
(ii) defective buble from 2 to 6 ?
(iii) defective bulbs less than 4 ?

Answer 1

700 carton were examined for defective bulbs. One carton was selected at random.
(i) Let `E_(1)` be the event that selected carton has no defective bulb.
We see that the number of times the event happened = 400
`:." P"(E_(1))=("Number of trials in which the event happened")/("Total number of trials")=(400)/(700)=(4)/(7)`
(ii) Let `E_(2)` be the event that selected carton has defective bulbs from 2 to 6.
We see that the number of times the event happened
`=48+41+18+8+3=118`
`:." P"(E_(2))=("Number of trials in which the event happened")/("Total number of trials")=(118)/(700)=(59)/(350)`
(iii) Let `E_(3)` be the event that selected carton has defective bulbs less than 4.
We see that the number of times the event happened
`=400+180+48+41=669`
`:." P"(E_(3))=("Number of trials in which the event happened")/("Total number of trials")=(669)/(700)`