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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 20
Total: 101
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.
Solution:  
Total oranges are 15, in which 12 are good ones & 3 are bad ones. E1 be the event of drawing first orange (good ones), E2 be the event of drawing second orange (good ones) & E3 be the event of drawing third orange (good ones). Then P(E1)=
12
15
,P(E2|E1)=
11
14
, P(E3|E2|E1)=
10
13
 .
Hence, the required probability P(E1∩E2∩E3)=
12
15
×
11
14
×
10
13
=
44
91
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