CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

The question is from Permutation and Combination. This question is about Selection. We need to compute the probability of selecting a bag then a ball from it. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

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

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: Clue - FInd the number of rearrangements and then focus on the number of digits

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) = $\frac{17}{35}\\$

The question is "If from the selected bag one ball is drawn, then what is the probability that the ball drawn is red?"

Hence the answer is "$\frac{17}{35}\\$"

Choice D is the correct answer.