| There are 5 red balls, 4 yellow balls and 3 green balls in a basket. If 3 balls are drawn at random, what is the probability that at least 2 of them are green in colour? [IBPS (SO) 2014] |
A) 1/11
B) 13/55
C) 3/11
D) 11/55
E) 7/55
Correct Answer: E
Solution :
| Here, total balls in the bag |
| = 5 red + 4 yellow + 3 green = 12 balls |
| Now, 3 balls chosen at random in which two bate are green in colour. |
| Selecting 3 balls \[={}^{9}{{C}_{1}}\times {}^{3}{{C}_{2}}+{}^{3}{{C}_{3}}\] |
| Sample space \[={}^{12}{{C}_{3}}\] |
| P (getting at least 2 green balls) |
| \[=\,\,\frac{{}^{9}{{C}_{1}}\times {}^{3}{{C}_{2}}+{}^{3}{{C}_{3}}}{{}^{12}{{C}_{3}}}\,\,=\,\,\frac{9\times 3+1}{220}\,\,=\,\,\frac{28}{220}\,\,=\,\,\frac{7}{55}\] |
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