Question

A bag contains 6 white and 4 black balls. If 2 balls are drawn from the bag, what is the probability that both are white?

• A. 0.25
• B. 0.33
• C. 0.4
• D. None of these

Hint:

Use \(\frac{\binom{6}{2}}{\binom{10}{2}}\) to find the chance both balls drawn are white.

Answer 1

The Correct Option is B

Step 1: Treat the two draws one after another instead of using combinations.
There are 10 balls in total, 6 white and 4 black. We draw one ball, do not replace it, then draw a second ball.

Step 2: Find the probability the first ball is white.
Out of 10 balls, 6 are white:
\[ P(\text{first white}) = \frac{6}{10} \]

Step 3: Find the probability the second ball is also white, given the first was white.
After removing one white ball, 9 balls remain, of which 5 are white:
\[ P(\text{second white} \mid \text{first white}) = \frac{5}{9} \]

Step 4: Multiply the two probabilities, since both events must happen in sequence.
\[ P(\text{both white}) = \frac{6}{10} \times \frac{5}{9} = \frac{30}{90} \]

Step 5: Simplify and compare with the options.
\[ \frac{30}{90} = \frac{1}{3} \approx 0.33 \]
This is the same result as the combinations approach, confirming the answer without needing to count total pairs directly.
\[ \boxed{0.33} \]