A) \[\frac{9}{87}\]
B) \[\frac{12}{87}\]
C) \[\frac{15}{87}\]
D) \[\frac{47}{87}\]
Correct Answer: D
Solution :
The total number of ways of choosing two numbers out of \[1,\,\,2,\,\,3,\,\,.........,\,30\] is \[{}^{30}{{C}_{2}}=435.\] Since \[{{a}^{2}}-{{b}^{2}}\] is divisible by 3 if either \[a\] and b both are divisible by 3 or none of a and b is divisible by 3. Thus the favourable number of cases = \[^{10}{{C}_{2}}+{{\,}^{20}}{{C}_{2}}=235\]. Hence the required probability = \[\frac{235}{435}=\frac{47}{87}\].
You need to login to perform this action.
You will be redirected in
3 sec
