Question

When a two digit number is rotated by ${180}^{\circ }$ a different two digit number is obtained. What is the probability of such an occurrence?

• A.
• B.
• C.
• D.
• E.

Answer 1

The correct option is A

Total 2 digit numbers : $9\times 10=90.$
Digits which are symmetrical : 1, 8, 0.
Digits which form a complementary symmetrical pair (i.e. when one is rotated, the other is obtained) – 6, 9.
When 0 is used as ten’s digit, it is a 1 digit no.
When 0 is used as unit’s digit and the no. is rotated by 180, it becomes a 1 digit no. So, we won’t use 0 in the 2-digit number.
Total possible nos. using digits 1, 8, 6, 9 : 4 $\times$ 4 = 16
But the nos. 11, 88, 69, 96 when rotated by 180 reveals the same no. again.
$\therefore$ Probability = $\frac{12}{90}=\frac{2}{15}$