Question:
In a box, there are \(8\) red, \(7\) blue and \(6\) green balls. One ball is picked randomly. The probability that it is neither red nor green is
In a box, there are \(8\) red, \(7\) blue and \(6\) green balls. One ball is picked randomly. The probability that it is neither red nor green is
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For probability questions, first identify the favorable outcomes carefully and then divide by the total number of possible outcomes.
Updated On: Jun 22, 2026
- \(\dfrac{1}{3}\)
- \(\dfrac{3}{4}\)
- \(\dfrac{7}{19}\)
- \(\dfrac{8}{21}\)
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The Correct Option is A
Solution and Explanation
Step 1: Find the total number of balls.
The box contains
\[ 8 \text{ red balls},\quad 7 \text{ blue balls},\quad 6 \text{ green balls} \] Therefore, total number of balls is
\[ 8+7+6=21 \]
Step 2: Find the favorable outcomes.
The probability that the selected ball is neither red nor green means the ball must be blue.
Number of blue balls \(=7\).
Thus, the number of favorable outcomes is
\[ 7 \]
Step 3: Apply the probability formula.
Probability is given by
\[ P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] Hence,
\[ P(\text{neither red nor green}) = \frac{7}{21} \] \[ = \frac{1}{3} \]
Step 4: Final conclusion.
Therefore, the required probability is
\[ \boxed{\frac{1}{3}} \]
The box contains
\[ 8 \text{ red balls},\quad 7 \text{ blue balls},\quad 6 \text{ green balls} \] Therefore, total number of balls is
\[ 8+7+6=21 \]
Step 2: Find the favorable outcomes.
The probability that the selected ball is neither red nor green means the ball must be blue.
Number of blue balls \(=7\).
Thus, the number of favorable outcomes is
\[ 7 \]
Step 3: Apply the probability formula.
Probability is given by
\[ P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] Hence,
\[ P(\text{neither red nor green}) = \frac{7}{21} \] \[ = \frac{1}{3} \]
Step 4: Final conclusion.
Therefore, the required probability is
\[ \boxed{\frac{1}{3}} \]
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