Q77 / 160 · TS EAMCET 2023 (13 May Shift 2) · Mathematics

A bag contains 3 red, 5 black and 7 blue balls. If three balls are drawn at random simultaneously from the bag then the probability of getting at least two blue balls is

  • Correct answer
    A
    $\frac{29}{65}$
  • B
    $\frac{29}{130}$
  • C
    $\frac{9}{65}$
  • D
    $\frac{9}{130}$

Solution

Atleast 2 blue $=$ ( 2 blue and 1 other) or ( 3 blue) $$ \begin{aligned} & P \text { (atleast 2 blue) }=\frac{{ }^7 C_2 \times{ }^8 C_1}{{ }^{15} C_3}+\frac{{ }^7 C_3}{{ }^{15} C_3} \\ & =\frac{{ }^7 C_2 \times{ }^8 C_1+{ }^7 C_3}{{ }^{15} C_3} \\ & =\frac{168+35}{7 \times 5 \times 13}=\frac{29}{65} . \end{aligned} $$

Hence, the correct answer is option: 'A'.

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