# Questionbank: Permutation and Probability

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Clue - FInd the number of rearrangements and then focus on the number of digits

## Sum of Rearrangements

Q.29: A bag contains 4 red and 3 black balls. A second bag contains 2 red and 3 black balls. One bag is selected at random. If from the selected bag one ball is drawn, then what is the probability that the ball drawn is red?
1. ${\frac{39}{70}}$

2. ${\frac{41}{70}}$

3. ${\frac{29}{70}}$

4. ${\frac{17}{35}}$

Choice D. ${\frac{17}{35}}$

## Detailed Solution

Let Red balls be 'r' and brown balls be 'b'

P(r) = p(b1) * p(r) + p(b2) * p(r)

P(R) = $\frac{1}{2} * \frac{4}{7} + \frac{1}{2} * \frac{2}{5}$

P(R) = $\frac{17}{35}$

Correct Answer : ${\frac{17}{35}}$

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