GMAT® Quant Practice : Probability

Concept: Probability of selecting a ball from one of the two bags.

This GMAT quant practice question is a discrete probability problem solving question. The concept tested in this question is to find the probability of selecting a red ball from one of the two bags.

Question: Bag x contains 3 red and 5 black balls and bag y contains 4 red and 4 black balls. One bag is selected at random and from the selected bag one ball is drawn. What is the probability that the ball drawn is red?

  1. \\frac{7}{8})
  2. \\frac{7}{16})
  3. \\frac{3}{16})
  4. \\frac{4}{5})
  5. \\frac{9}{16})

Explanatory Answer

Video explanation will be added soon

Bags x and y are equally likely to be selected.
The probability of selecting a red ball = probability of selecting a red ball from bag x + probability of selecting a red ball from bag y.

Probability of selecting a red ball from bag x = probability of selecting bag x * probability of selecting red ball from it.
= \\frac{1}{2}) * \\frac{3}{8}) = \\frac{3}{16})

Probability of selecting a red ball from bag y = probability of selecting bag y * probability of selecting red ball from it.
= \\frac{1}{2}) * \\frac{4}{8}) = \\frac{4}{16})

Probability that the ball drawn is red = \\frac{3}{16}) + \\frac{4}{16}) = \\frac{7}{16})

The correct choice is (B) and the correct answer is \\frac{7}{16}).

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