| A bag contains 13 white and 7 black balls. Two balls are drawn at random. What is the probability that they are of the same colour? [IBPS (PO) 2012] |
A) \[\frac{41}{190}\]
B) \[\frac{21}{190}\]
C) \[\frac{59}{190}\]
D) \[\frac{99}{190}\]
E) \[\frac{77}{190}\]
Correct Answer: D
Solution :
| The number of balls in bag \[=13+7=20\] |
| \[\therefore \] \[n\,(S)={}^{20}{{C}_{2}}=190\] |
| For same colour of ball, \[n\,({{E}_{1}})={}^{13}{{C}_{2}}=78\] |
| and \[n\,({{E}_{2}})={}^{7}{{C}_{2}}=21\] |
| Hence, required probability, |
| \[P(E)=\frac{n\,({{E}_{1}})}{n\,(S)}+\frac{n\,({{E}_{2}})}{n\,(S)}=\frac{78}{190}+\frac{21}{190}=\frac{99}{190}\] |
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