Question:
A jar contains 7 black balls, 6 yellow balls, 4 green balls and 3 red balls. All of them are of same size and weight. If a ball is drawn at random, then the probability of the ball being red is
A jar contains 7 black balls, 6 yellow balls, 4 green balls and 3 red balls. All of them are of same size and weight. If a ball is drawn at random, then the probability of the ball being red is
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Logic Tip: The phrase "same size and weight" is explicitly included in probability problems to guarantee that every single ball has an equal, unbiased chance of being selected (i.e., the outcomes are "equally likely").
Updated On: Apr 30, 2026
- $\frac{1}{5}$
- $\frac{3}{20}$
- $\frac{1}{10}$
- $\frac{3}{10}$
- $\frac{1}{20}$
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The Correct Option is B
Solution and Explanation
Concept:
The fundamental classical probability formula states that the probability of an event $E$ occurring is the number of outcomes favorable to $E$ divided by the total number of equally likely outcomes in the sample space. $$P(E) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Possible Outcomes}}$$
Step 1: List the quantities of each ball type.
Black balls = 7 Yellow balls = 6 Green balls = 4 Red balls = 3
Step 2: Calculate the total number of balls.
Add all the individual ball counts together to find the size of the total sample space: $$\text{Total Balls} = 7 + 6 + 4 + 3$$ $$\text{Total Balls} = 20$$
Step 3: Identify the number of favorable outcomes.
The event in question is drawing a "red ball." The number of red balls in the jar is exactly 3. $$\text{Favorable Outcomes} = 3$$
Step 4: Set up the probability fraction.
Substitute the values from Step 2 and Step 3 into the probability formula: $$P(\text{Red}) = \frac{\text{Red Balls}}{\text{Total Balls}}$$
Step 5: Calculate the final probability.
$$P(\text{Red}) = \frac{3}{20}$$ This fraction cannot be simplified further. Hence the correct answer is (B) $\frac{3{20}$}.
The fundamental classical probability formula states that the probability of an event $E$ occurring is the number of outcomes favorable to $E$ divided by the total number of equally likely outcomes in the sample space. $$P(E) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Possible Outcomes}}$$
Step 1: List the quantities of each ball type.
Black balls = 7 Yellow balls = 6 Green balls = 4 Red balls = 3
Step 2: Calculate the total number of balls.
Add all the individual ball counts together to find the size of the total sample space: $$\text{Total Balls} = 7 + 6 + 4 + 3$$ $$\text{Total Balls} = 20$$
Step 3: Identify the number of favorable outcomes.
The event in question is drawing a "red ball." The number of red balls in the jar is exactly 3. $$\text{Favorable Outcomes} = 3$$
Step 4: Set up the probability fraction.
Substitute the values from Step 2 and Step 3 into the probability formula: $$P(\text{Red}) = \frac{\text{Red Balls}}{\text{Total Balls}}$$
Step 5: Calculate the final probability.
$$P(\text{Red}) = \frac{3}{20}$$ This fraction cannot be simplified further. Hence the correct answer is (B) $\frac{3{20}$}.
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