Question bank/JEE Main/Mathematics

An urn contains 5 red and 2 green balls, one ball is chosen from
urn, if it is red then a green ball is put back into Box, and if it is
green then a red ball is put in to box (previous ball was not put in
that box), then a second ball is drawn the probability that it is red
ball, is

A$\frac{32}{49}$B$\frac{17}{49}$C$\frac{15}{49}$D$\frac{36}{49}$

Show answer and solution▾

R1 [IMAGE] first ball drawn is a red ball drawn
is red
P(R_2) = P(R_1).
$= \frac{5}{7} \cdot \frac{4}{7} + \frac{2}{7} \cdot \frac{6}{7} = \frac{20}{49} + \frac{12}{49} = \frac{32}{49}$

Source: Grass-G / M-11 Mathematics Paper-2 1Nov.docx