Two different balls are drawn from hat W. |
Two different balls are drawn from hat B. |
One ball is drawn from each hat. |
The probability of getting at least one white ball, is |
A) \[\frac{1}{2}\]
B) \[\frac{1}{4}\]
C) \[\frac{22}{27}\]
D) \[\frac{21}{27}\]
Correct Answer: C
Solution :
P (atleast) one white ball) \[=P({{S}_{1}})\,+P({{S}_{2}})\,+P({{S}_{3}})\] ?.(3) Where .?(2) \[P({{S}_{2}})\,=\frac{1}{3}\,\left[ \frac{^{1}{{C}_{1}}\,{{\times }^{2}}{{C}_{1}}}{^{3}{{C}_{2}}} \right]\,=\frac{2}{9}\] ?(3) and \[P({{S}_{3}})\,=\frac{1}{3}\,\left[ 1-\frac{1}{3}\times \frac{2}{3} \right]\,=\frac{1}{3}\,\left( \frac{7}{9} \right)\,=\frac{7}{27}\,\] ?(4) \[\therefore \] Using (2), (3) and (4) in (1), we get P(atleast one white ball) \[=\frac{1}{3}\,+\frac{2}{9}\,+\frac{7}{27}\,=\frac{9+6+7}{27}=\frac{22}{27}\]You need to login to perform this action.
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