Test Index

Probability Part 2

Section: Mathematics

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Question : 39 of 100

Marks: +1, -0

Let

N

denote the sum of the numbers obtained when two dice are rolled. If the probability that

2^{N} < N

\;\frac{m}{n}

m

n

are coprime, then

4 m - 3 n

[10-Apr-2023 shift 1]

12
8
10
6

Solution:

2^{N} < N

! is satisfied for

N \ge 4

Required probability

P(N \ge 4)=1-P(N < 4)

N=1

(Not possible)

N=2(1,1)

\Rightarrow P(N=2)=\;\frac{1}{36}

N=3(1,2),(2,1)

\Rightarrow P(N=3)=\;\frac{2}{36}

P(N<4)=\;\frac{1}{36}+\;\frac{2}{36}=\;\frac{3}{36}

\therefore P(N \ge 4)=1-\;\frac{3}{36}=\;\frac{33}{36}=\;\frac{11}{12}=\;\frac{m}{n}

\Rightarrow m=11,\;n=12

\therefore 4 m - 3 n = 4(11) - 3(12) = 8

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