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Two different numbers are selected at random from $1, 2, 3, 4........100$ and are multiplied, then the probability (correct upto two place of decimals) that the product thus obtained is divisible by $3$ , is
Option: 1
$0.22$

Option: 2
$0.33$

Option: 3
$0.44$

Option: 4
$0.55$

Answers (1)

best_answer

For selecting any two numbers out of $100=^{100}C_{2}$

$P\left ( S \right )=^{100}C_{2}$

Now number of ways for getting product of two number is divisible by $'3'=^{33}C_{2}+^{33}C_{1}\times ^{67}C_{1}$

So $P\left ( E \right )=\frac{^{33}C_{2}+33\times67}{^{100}C_{2}}=0.55$

(Where 33 is total number from 1 to 100 which is multiple of 3)

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vinayak

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