Question: 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. 29/70
2. 17/35
3. 19/35
4. 39/70
5. 41/70

Correct Answer: (B)
Solution and Explanation:
Approach Solution 1:

The problem statement informs that:

Given:

• A bag contains 4 red and 3 black ball
• A second bag contains 2 red and 3 black balls
• One bag is selected at random.

Find Out:

• The probability that the ball drawn is red if one ball is drawn from the chosen bag.

Let there be 2 bags B1 and B2.
First, we must choose a bag.
The probability of choosing a bag is P(B1) = P(B2) = 1/2

Now, as per the question, both the bags holds the red ball. The chance of choosing a red ball is mainly based on the bag chosen.

Therefore, the probability of selecting a red ball is:

P (R) = P (B1) * P (R/B1) + P (B2) * P (R/B2),
where P(R/B1) & P(R/B2) indicates the probability of choosing a red ball given in bag 1 and bag 2 respectively.
Therefore, P(R/B1) = 4/7 & P(R/B2) = 2/5.
Thus, P(R) = 1/2* 4/7 + 1/2*2/5 = 17/35
Hence, the probability that the ball drawn is red = 17/35

Approach Solution 2:

The problem statement implies that:

Given:

• A bag contains 4 red and 3 black ball
• A second bag contains 2 red and 3 black balls
• One bag is selected at random.

Find Out:

• The probability that the ball drawn is red if one ball is drawn from the chosen bag.

In bag 1, we can say:
Red ball = 4/7
In bag 2, we can say:
Red ball = 2/5
Therefore, Total Probability = 4/7+2/5 = 34/35
and there is a probability of choosing either bag 1 or bag 2= 1/2;
Hence, the probability that the ball drawn is red = 34/35 * 1/2 = 17/35

“A bag contains 4 red and 3 black balls. A second bag contains 2 red''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions test the basic math concepts and calculative skills of the candidates to solve mathematical problems. GMAT Quant practice papers help the candidates to analyse varieties of types of questions that will brush up their mathematical learning.

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