Question

A divisor of 1200 is selected at random. Find the probability that it is even.

• A. $\frac{4}{5}$
• B. $\frac{3}{5}$
• C. $\frac{3}{4}$
• D. $\frac{12}{13}$

Answer 1

The correct option is A

$\frac{4}{5}$

$1200=2^4\times 3^2\times 5^2$

For divisors of 1200, 2 can be chosen in 5ways i.e.,

$2^0,2^1,2^2,2^3,2^4$

Similarly, 3 and 5 can be chosen in 3 ways each i.e.,

$3^0,3^1,3^2\text{and}{5}^0,5^1,5^2$

$\therefore$ Total no.of divisors of $1200=5\times 3\times 3$

For getting even divisors of 1200, we have to choose 2 at least once; Thus, the number of

ways in which 2 can be chosen is $4i.e.,2^1,2^2,2^3,2^4$

While 3,5 can be chosen in 3 ways each i.e., $3^0,3^1,3^2$ and $5^0,5^1,5^2$

$\therefore$ Number of even divisors of $1200=4\times 3\times 3$

Probability =$\frac{\text{Number~of~even~divisors}}{\text{Total~number~of~divisors}}=\frac{4\times 3\times 3}{5\times 3\times 3}$

$=\frac{4}{5}$