Q81 / 160 · TS EAMCET 2018 (04 May Shift 2) · Mathematics

The probability of securing a success in a trial is three times that of a failure. The probability of getting atleast 4 successes in 5 trials is

  • A
    $\frac{649}{1024}$
  • Correct answer
    B
    $\frac{81}{128}$
  • C
    $\frac{27}{64}$
  • D
    $\frac{243}{1024}$

Solution

$P=\frac{3}{4}, q=\frac{1}{4}$ getting atleast 4 successes in 5 trial is Now, getting atleast 4 successes is $$ \begin{aligned} & { }^5 C_4 p^4 q^1+{ }^5 C_5 p^5 q^0 \\ & \Rightarrow \quad \frac{5 !}{4 !} \cdot\left(\frac{3}{4}\right)^4\left(\frac{1}{4}\right)+\frac{5 !}{5 ! 0 !} \cdot\left(\frac{3}{4}\right)^5 \end{aligned} $$ So, $\quad 5 \cdot\left[\frac{3}{4}\right]^4\left(\frac{1}{4}\right)+\left(\frac{3}{4}\right)^5$ So, $\quad\left(\frac{3}{4}\right)^4\left[\frac{5}{4}+\frac{3}{4}\right] \Rightarrow \frac{81}{256} \cdot(2) \Rightarrow \frac{81}{128}$

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

Relevant Questions