Question

An urn contains 4 red and 5 white balls. Two balls are drawn one after the other without replacement. Find the probability that both the balls are red.

• A. \( \dfrac{5}{6} \)
• B. \( \dfrac{1}{6} \)
• C. \( \dfrac{2}{9} \)
• D. \( \dfrac{4}{9} \)

Hint:

For events without replacement, always adjust the total number of outcomes after each draw.

Answer 1

The Correct Option is B

Step 1: Find the probability of drawing a red ball first.
Total number of balls \(= 4 + 5 = 9\). \[ P(\text{First red}) = \frac{4}{9} \]
Step 2: Find the probability of drawing a red ball second.
After one red ball is drawn, remaining red balls \(= 3\) and total balls \(= 8\). \[ P(\text{Second red}) = \frac{3}{8} \]
Step 3: Find the required probability.
Since both events must occur: \[ P(\text{Both red}) = \frac{4}{9} \times \frac{3}{8} = \frac{12}{72} = \frac{1}{6} \]
Step 4: Final conclusion.
The probability that both balls drawn are red is \( \dfrac{1}{6} \).