$\begin{array}{1 1}(A)\;\large\frac{2}{5}\\(B)\;\large\frac{3}{5}\\(C)\;\large\frac{4}{5}\\(D)\;\large\frac{7}{5}\end{array} $

- Required probability =$\large\frac{n(E)}{n(S)}$

Step 1:

4 digit number greater than 5000 are to be formed

Digits -0,1,3,5,7

Number to be divisible by 5

$\therefore$ A number can be divisible by 5 only when its units digit is 0,5

Step 2:

The digits are repeated

Total number of outcomes will be :

Since the number has to be greater than 5000,the thousand digit should be 5 or 7 and rest three digit can be any of the number.Total number of digits =5

$\therefore 5\Rightarrow 5\times 5\times 5=125$

$7\Rightarrow 5\times 5\times \times 5=125$

$\therefore$ Total 4 digit numbers n(S)=250

Step 3:

Number of favorable outcomes :

For a number to be divisible by 5.The unit digit should be 0 or 5 and the thousand digit is fixed as 5 or 7.

$\therefore$ Total number of favorable outcomes n(E)=25+25+25+25

$\Rightarrow 100$

Step 4 :

$\therefore$ Required probability =$\large\frac{n(E)}{n(S)}$

$\Rightarrow \large\frac{100}{250}$

$\Rightarrow \large\frac{2}{5}$

Hence (A) is the correct answer.

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So, Total No. of Outcomes will be 250-1=249

and No. of Favorable Events will be 100-1=99

Therefore, Probability is 99/249 = 33/83