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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Probability

NDA 2023 · Mathematics · Probability

One bag contains 3 white and 2 black balls, another bag contains 2...

One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the first bag and put it into the second bag and then a ball is drawn from the second bag. What is the probability that it is white?

Options

  1. A1635\frac{16}{35}
  2. B3370\frac{33}{70}
  3. C310\frac{3}{10}
  4. D170\frac{1}{70}

Correct answer

A. 1635\frac{16}{35}

Step-by-step solution


When 2 balls are drawn from I, it can be done as both black, both white or 1 black 1 white. Now in such cases, new number of balls will be
Total Probability =(2C25C2×27)+(2C1×3C15C2×37)+(3C25C2×47)=3270=1635=\left(\frac{{ }^2 C_2}{{ }^5 C_2} \times \frac{2}{7}\right)+\left(\frac{{ }^2 C_1 \times{ }^3 C_1}{{ }^5 C_2} \times \frac{3}{7}\right)+\left(\frac{{ }^3 C_2}{{ }^5 C_2} \times \frac{4}{7}\right)=\frac{32}{70}=\frac{16}{35}.
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