Q79 / 160 · TS EAMCET 2019 (03 May Shift 1) · Mathematics

A box contains 10 mangoes out of which 4 are spoiled. 2 mangoes are taken together at random. If one of them is found to be good, then the probability that the other is also good, is

  • A
    $\frac{1}{3}$
  • B
    $\frac{2}{3}$
  • C
    $\frac{8}{15}$
  • Correct answer
    D
    $\frac{5}{13}$

Solution

Let $A$ be the event that the first mango is good and $B$ be the event that second is good. $\therefore$ Required probability $=P\left(\frac{B}{A}\right)=\frac{P(A \cap B)}{P(A)}$ $$ \begin{gathered} P(A)=\frac{{ }^6 C_2}{{ }^{10} C_2}+\frac{{ }^6 C_1 \times{ }^4 C_1}{{ }^{10} C_2} \\ P(A \cap B)=\frac{{ }^6 C_2}{{ }^{10} C_2} \\ \therefore P\left(\frac{B}{A}\right)=\frac{{ }^6 C_2}{{ }^6 C_2+{ }^6 C_1 \times{ }^4 C_1}=\frac{15}{15+24}=\frac{15}{39}=\frac{5}{13} \end{gathered} $$

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

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