All the 4 numbers should be odd numbers as their multiplication ends with odd number. So, probability of randomly choosing an odd number is 1∕2. Also the product should not end with digit 5. So probability of choosing a multiple of 5 is 1∕5. So, probability of choosing a non-multiple of 5 is 4∕5. Thus probability of choosing a number which is odd and not multiple of 5 is
4
5
×
1
2
=
2
5
. So, probability of choosing 4 such numbers randomly whose product end with 1,3,7,9 is =