Q. 285.0( 4 Votes )
A box contains 100bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that:
(i) all 10 are defective
(ii) all 10 are good
(iii) at least one is defective
(iv) none is defective
Answer :
given: box with 100 bulbs of which, 20 are defective
formula: 
ten bulbs are drawn at random for inspection, therefore
total possible outcomes are 100C10
therefore n(S)= 100C10
(i) let E be the event that all ten bulbs are defective
n(E)= 20C10
(ii) let E be the event that all ten good bulbs are selected
n(E)= 80C10
(iii) let E be the event that at least one bulb is defective
E= {1,2,3,4,5,6,7,8,9,10} where 1,2,3,4,5,6,7,8,9,10 are the number of defective bulbs
Let E’ be the event that none of the bulb is defective
n(E’) = 80C10
Therefore,
P(E)=1-P(E’)
(iv) let E be the event that none of the selected bulb is defective
n(E)= 80C10
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