A) \[\frac{3}{44}\]
B) \[\frac{5}{55}\]
C) \[\frac{52}{55}\]
D) \[\frac{41}{44}\]
E) \[\frac{4}{33}\]
Correct Answer: D
Solution :
Let S be the sample space. Then, n(S) = Number of ways of drawing three marbles out of \[12={{\,}^{12}}{{C}_{3}}\] \[=\frac{12\times 11\times 10}{3\times 2}=220\] Let E be the event of drawing 3 balls of the same colour. Then, n= event of drawing (3 balls out of 5) or (3 balls out of 4) or (3 balls out of 3) \[\therefore \]\[n(E)=({{\,}^{5}}{{C}_{3}}+{{\,}^{4}}{{C}_{3}}+{{\,}^{3}}{{C}_{3}})=\frac{5\times 4}{2\times 1}=+\,4+1=15\] \[\therefore \]\[P(E)=\frac{n(E)}{n(S)}=\frac{15}{20}=\frac{3}{44}\] \[\therefore \]Reqd probability \[=1-\frac{3}{44}=\frac{41}{44}\]
You need to login to perform this action.
You will be redirected in
3 sec
