Question

A bag contains some red and some white balls. A ball is drawn at random from the bag. If the probability of getting a red ball is \(\frac{2}{7}\), then the probability of getting a white ball is

• A. \(\frac{1}{14}\)
• B. \(\frac{5}{7}\)
• C. \(\frac{1}{7}\)
• D. \(\frac{2}{7}\)

Hint:

For any two complementary outcomes, if the probability of one is \(\frac{x}{y}\), the probability of the other is always \(\frac{y - x}{y}\).
Here, \(\frac{7 - 2}{7} = \frac{5}{7}\), which can be determined mentally in a split second!

Answer 1

The Correct Option is B

Step 1: Understand the problem setup.
A bag contains only red and white balls. The probability of drawing a red ball is \(\frac{2}{7}\). We need the probability of drawing a white ball.
Step 2: Recall the complementary event rule.
For complementary events, \(P(\text{red}) + P(\text{white}) = 1\).
Step 3: Substitute the known value.
\(\frac{2}{7} + P(\text{white}) = 1\).
Step 4: Solve for P(white).
\(P(\text{white}) = 1 - \frac{2}{7} = \frac{5}{7}\).
Step 5: Verify the result makes sense.
\(\frac{2}{7} + \frac{5}{7} = \frac{7}{7} = 1\). The probabilities sum to 1, which is correct.
Step 6: Select the correct option.
\(P(\text{white}) = \frac{5}{7}\), which is option 2.
\[ \boxed{\dfrac{5}{7}} \]