Q. 134.8( 5 Votes )

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale otherwise it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.

Answer :

Number of oranges the box contains = 15


Number of good oranges = 12


Number of bad oranges = 3


Probability that box is approved for sale


= Probability that first orange is good × probability that second orange is good, given first is good × probability that third orange is good, given first two are good


Let A represents a good orange


Then P(A)=P(getting first orange as good)


And


P(A│A)=P(getting second orange good, given first is good)


(as now there are 11 good oranges left out of 14 total oranges as one good orange is already drawn in first draw and are not replaced)


And also,


P(AA│A)=P(getting third orange good, given first two are good)


(as now there are 10 good oranges left out of 13 total oranges as two good orange is already drawn in first draw and are not replaced)


So the probability that box is approved for sale is




Therefore probability that box is approved for sale is


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