Question

Probability that the second ball is red, given the first was blue (3 red and 5 blue balls, without replacement).

• A. \(3/7\)
• B. \(3/8\)
• C. \(2/7\)
• D. \(5/14\)

Hint:

Without replacement means the denominator decreases after each draw.

Answer 1

The Correct Option is A

Concept: This is a conditional probability problem. Since balls are drawn without replacement, the total number of balls changes after the first draw.

Step 1: Write initial number of balls Initially: \[ 3\text{ red balls} \] \[ 5\text{ blue balls} \] Total balls: \[ 3+5=8 \]

Step 2: Apply given condition It is given that the first ball drawn was blue. So one blue ball is removed. Remaining balls: \[ 3\text{ red} \] \[ 4\text{ blue} \] Total remaining: \[ 7 \]

Step 3: Find required probability Probability that second ball is red: \[ P(\text{Red}) = \frac{\text{Number of red balls remaining}} {\text{Total balls remaining}} \] \[ =\frac37 \] Final Answer: \[ \boxed{\frac37} \]