The probability of getting a double six in one throw of two dice =
1
6
×
1
6
=
1
36
∴ p =
1
36
, q = 1 - p = 1 -
1
36
=
35
36
Now, (p+q)m = qn+
n
‌
C1qn−1p +
n
‌
C2qn−2p2 + ... +
n
‌
Crqn−rpr + ... + pn The probability of getting atleast one double six in n throws with two dice. = (q+p)n−qn = 1 - qn = 1 - (
35
36
)n ∴ 1 - (
35
36
)n > 0.99 ⇒ (
35
36
)n < 0.01 ⇒ n(log 35 - log 36) < log 0.01 ⇒ n[15441 - 15563] < -2 ⇒ - 0.0122n < - 2 ⇒ 0.0122n > 2 → n > 163.9 So, the least value of n is 164.