JEE Main 2026 — Apr 5, Shift 1 — Mathematics solution

JEE Main2026Apr 5, Shift 1Mathematics

A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is :

A
$\frac{7}{10}$
B
$\frac{10}{17}$
C
$\frac{12}{19}$
D
$\frac{7}{19}$

Solution

Let $E_{1}$ denote the letter being from KANPUR and $E_{2}$ from ANANTPUR, each with prior $\frac{1}{2}$ .

KANPUR has $6$ letters and so $5$ pairs of consecutive letters: KA, AN, NP, PU, UR. Exactly one pair is AN, giving $P (AN ∣ E_{1}) = \frac{1}{5}$ .

ANANTPUR has $8$ letters and $7$ consecutive pairs: AN, NA, AN, NT, TP, PU, UR. Two of these are AN, giving $P (AN ∣ E_{2}) = \frac{2}{7}$ .

By Bayes' theorem,

$P (E_{2} ∣ AN) = \frac{\frac{1}{2} \cdot \frac{2}{7}}{\frac{1}{2} \cdot \frac{1}{5} + \frac{1}{2} \cdot \frac{2}{7}} = \frac{2/7}{1/5 + 2/7} = \frac{2/7}{17/35} = \frac{10}{17}$ .

← Back to full paper

Practice more Mathematics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →