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?

- \\frac{7}{8})
- \\frac{7}{16})
- \\frac{3}{16})
- \\frac{4}{5})
- \\frac{9}{16})

#### Video Explanation

Scroll for explanatory answer text#### Explanatory Answer

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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