Question -
Answer -
Given: A box contains100bulbs, 20 of which are defective.
By using the formula,
P (E) = favourableoutcomes / total possible outcomes
Ten bulbs are drawn atrandom for inspection,
Total possibleoutcomes are┬а100C10
n (S) =┬а100C10
(i)┬аLet E be theevent that all ten bulbs are defective
n (E) =┬а20C10
P (E) = n (E) / n (S)
=┬а20C10┬а/┬а100C10
(ii)┬аLet E be theevent that all ten good bulbs are selected
n (E) =┬а80C10
P (E) = n (E) / n (S)
=┬а80C10┬а/┬а100C10
(iii)┬аLet E be theevent 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 defectivebulbs
Let EтА▓ be the eventthat none of the bulb is defective
n (EтА▓) =┬а80C10
P (EтА▓) = n (EтА▓) / n(S)
=┬а80C10┬а/┬а100C10
So, P (E) = 1 тАУ P (EтА▓)
= 1 тАУ┬а80C10┬а/┬а100C10
(iv)┬аLet E be theevent that none of the selected bulb is defective
n (E) =┬а80C10
P (E) = n (E) / n (S)
=┬а80C10┬а/┬а100C10