Q109 / 160 · AP EAMCET 2014 · Mathematics

A six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be 7 . The probability that the number 3 has appeared atleast once, is

  • A
    $\frac{1}{5}$
  • B
    $\frac{2}{5}$
  • Correct answer
    C
    $\frac{3}{5}$
  • D
    $\frac{4}{5}$

Solution

Sum of the dice is 7 . $$ \begin{aligned} & S=-\{(1,6),(6,1),(2,5),(5,2),(3,4),(4,3)\} \\ & \therefore n(S)=6 \end{aligned} $$ Let, $E=$ Event of getting atleast three 3 or a die $$ \therefore n(E)=2 $$ $$ \therefore \text { Required probability }=\frac{n(E)}{n(S)}=\frac{2}{6}=\frac{1}{3} $$

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

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