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STD 12 - 13. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 13. probability4 Marks
MCQ
One ticket is selected at random from $50$ tickets numbered $00,01,02, ... ,49.$ Then the probability that the sum ofthe digits on the selected ticket is $8$, given that the product of these digits is zero, equals:
  • A
    $\frac{1}{{50}}$
  • B
    $\frac{{14}}{{50}}$
  • C
    $\frac{5}{{14}}$
  • ✓
    $\frac{1}{{14}}$
✓

Answer

Correct option: D.
$\frac{1}{{14}}$
d
$S=\{00,01,02, \ldots, 49\}$

Let $A$ be the event that sum of the digits on the selected ticket is $8,$ then

$A=\{08,17,26,35,44\}$

Let $B$ be the event that the product of the digits is zero.

$B =\{00,01,02,03, \ldots, 09,10,20,30,40\} $

$\therefore$ $A \cap B =\{8\}$

$\therefore$ Required probability $=P\left(\frac{A}{B}\right)$

${=\frac{P(A \cap B)}{P(B)}=\frac{\frac{1}{50}}{\frac{14}{50}}} $

${=\frac{1}{14}}$

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