Q79 / 160 · TS EAMCET 2020 (11 Sep Shift 1) · Mathematics

A number is selected at random from the set $\{1,2, \ldots \ldots, 100\}$. Given that the number selected is divisible 2 , the probability that it is also divisible by 3 or 5 , is

  • A
    $\frac{26}{50}$
  • Correct answer
    B
    $\frac{23}{50}$
  • C
    $\frac{7}{50}$
  • D
    $\frac{13}{50}$

Solution

The number divisible by 2 in set $\{1,2,3, \ldots, 100\}$ are $E=\{2,4,6, \ldots, 100\}$ and the numbers in set $E$ are divisible by 3 or 5 are $\{6,10,12,18,20,24,30,36,40,42,48,50,54,60$, $66,70,72,78,80,84,90,96,100\}$ So, required probability is $=\frac{23}{50}$

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

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