Verified Solution • 2025–26 Session moderate

QJEEM18Ma94d7: JEE Main 2018 Mathematics - Class 12 JEEM18Ma94d7 Solution: A box 'A' contains white, red and black balls. Another box 'B'…

A box 'A' contains 22 white, 33 red and 22 black balls. Another box 'B' contains 44 white, 22 red and 33 black balls. If two balls are drawn at random, without eplacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is :

Multiple Choice Options

  • A 916{9 \over {16}}
  • B 716{7 \over {16}}
  • C 932{9 \over {32}}
  • D 78{7 \over {8}}

Step-by-Step Verified Solution

Probability of drawing a white ball and then a red ball

from bag B is given by 4C1×2C19C2{{{}^4{C_1} \times {}^2{C_1}} \over {{}^9{C_2}}} = 29{2 \over 9}

Probability of drawing a white ball and then a red ball

from bag A is given by 2C1×3C17C2{{{}^2{C_1} \times {}^3{C_1}} \over {{}^7{C_2}}} = 27{2 \over 7}

Hence, the probability of drawing a white ball and then

a red ball from bag B = 2927+29{{{2 \over 9}} \over {{2 \over 7} + {2 \over 9}}} = 2×718+14{{2 \times 7} \over {18 + 14}} = 716{7 \over {16}}

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