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: Note the total number of balls.
The bag has 6 white balls and 4 black balls, giving
\[ 6+4 = 10 \text{ balls in total} \]

Step 2: Find the total number of ways to draw 2 balls from 10.
Using combinations, since the order of drawing does not matter:
\[ \binom{10}{2} = \frac{10 \times 9}{2 \times 1} = 45 \]

Step 3: Find the number of ways to draw 2 white balls from the 6 white balls.
\[ \binom{6}{2} = \frac{6 \times 5}{2 \times 1} = 15 \]

Step 4: Divide the favourable outcomes by the total outcomes.
The probability that both balls drawn are white is
\[ P(\text{both white}) = \frac{\binom{6}{2}}{\binom{10}{2}} = \frac{15}{45} = \frac{1}{3} \]

Step 5: Convert to a decimal and match with the options.
\[ \frac{1}{3} = 0.333\ldots \approx 0.33 \]
This rules out option (a) 0.25 and option (c) 0.4, since neither is close to \(\frac{1}{3}\). Option (d) is not needed since a matching value exists.

Final Answer:
The probability that both balls are white is 0.33.
\[ \boxed{0.33} \]