VITEEE 2015 Paper

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.