From a collection of eight cards numbered 1 to 8 , if two cards are drawn at random, one after the other…
From a collection of eight cards numbered 1 to 8 , if two cards are drawn at random, one after the other with replacement, then the probability that the product of numbers that appear on the cards is a perfect square is
$\frac{3}{14}$
$\frac{6}{13}$
$\frac{3}{16}$
$\frac{1}{16}$
Solution
Let $A=\{(1,1),(1,4),(2,2),(2,8),(3,3)(4,1)$, $(4,4),(5,5),(6,6),(7,7),(8,2),(8,8)\}$
Whose product is square number
$\Rightarrow P(A)=\frac{12}{64}=\frac{3}{16}$