Two numbers are selected from the set ${1, 2, 3, 4, 5}$ with replacement. The probability that their product is divisible by $3$ can be written as $\frac{a^{2}}{b^{2}}$ . Then find the least positive integral value of $a$ is

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Solution

No. of favourable ways $= 9 {(1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (3, 1), (3, 2), (3, 4), (3, 5)}$
No. of total ways $= 5 \times 5 = 5^{2}$
$b = 5$
$9 = a^{2}$
$\Rightarrow a = 3$

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Two numbers are selected from the set {1,2,3,4,5} with replacement. The probability that their product is divisible by 3 can be written as a2b2. Then find the least positive integral value of a is

No. of favourable ways =9{(1,3),(2,3),(3,3),(4,3),(5,3),(3,1),(3,2),(3,4),(3,5)} No. of total ways =5×5=52 b=5 9=a2 ⇒a=3

Two numbers are selected from the set ${1, 2, 3, 4, 5}$ with replacement. The probability that their product is divisible by $3$ can be written as $\frac{a^{2}}{b^{2}}$ . Then find the least positive integral value of $a$ is

No. of favourable ways $= 9 {(1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (3, 1), (3, 2), (3, 4), (3, 5)}$
No. of total ways $= 5 \times 5 = 5^{2}$
$b = 5$
$9 = a^{2}$
$\Rightarrow a = 3$