ProbabilityHardBloom L3
Question
Two distinct numbers are selected from the numbers $\{ 1,2,3,\ldots.,9\}$, then the probability that their product is a perfect square is
Options
A.$\frac{1}{9}$
B.$\frac{2}{9}$
C.$\frac{1}{3}$
D.$\frac{4}{9}$
Solution
Sol. [Key Concept: Two distinct from $\{ 1,\ldots\}$ with the divisibility condition: count pairs.]
Favorable cases are (1, 4), (1, 9), (2, 8), (4, 9)
$$\therefore\ P = \frac{4}{\ ^{9}C_{2}} = \frac{1}{9}$$
Create a free account to view solution
View Solution FreeMore Probability Questions
A coin is tossed four times then the probability of obtaining at least one tail is -...Ram has 4 bats namely $B_{1},B_{2},B_{3},B_{4}$. He randomly selects one of the three bats which was not used in previou...If an integer q is chosen at random in the interval - 10 ≤ q ≤ 10, then the probability that the roots of th...There is a three volume dictionary among 40 books arranged on a shelf in random order. The probability of these volumes ...A, B, C are alternately and, in this order, rolling a fair die. The first one to roll an even number wins and the game i...