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 ^{100}C_{10}

therefore n(S)= ^{100}C_{10}

(i) let E be the event that all ten bulbs are defective

n(E)= ^{20}C_{10}

(ii) let E be the event that all ten good bulbs are selected

n(E)= ^{80}C_{10}

(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’) = ^{80}C_{10}

Therefore,

P(E)=1-P(E’)

(iv) let E be the event that none of the selected bulb is defective

n(E)= ^{80}C_{10}

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