Direction: A few statements have been given in each of the following questions. Analyse the given statements and answer whether the data given in the statements is sufficient to answer the question or not.
A box contains 20 tops of the same size and pattern. Each top is either white, black, or grey in colour. Find the number of black tops in the box.
Statement I: The probability of picking a black top is the same as the probability of picking a grey top.
Statement II: The number of grey tops is more than that of white tops.
Statement III: The probability of picking a white top is 20%.
Direction: A few statements have been given in each of the following questions. Analyse the given statements and answer whether the data given in the statements is sufficient to answer the question or not.
A box contains 20 tops of the same size and pattern. Each top is either white, black, or grey in colour. Find the number of black tops in the box.
Statement I: The probability of picking a black top is the same as the probability of picking a grey top.
Statement II: The number of grey tops is more than that of white tops.
Statement III: The probability of picking a white top is 20%.
- If the data in Statement I alone is sufficient.
- If data in all Statements I, II, and III is sufficient.
- If the data in only Statements I and III are sufficient.
- If the data in only Statement III is sufficient.
- If the data in all Statements I, II, and III are not sufficient.
The Correct Option is C
Solution and Explanation
Let the number of white, black, and grey tops in the box be \(x, y\), and \(z\), respectively.
From Statement I:
\(\frac{^yC1}{^{20}C1} = \frac{^zC1}{^{20}C1}\)
\(⇒ y = z\)
Not Sufficient
From Statement II:
\(z > x\)
Not Sufficient
From Statement III:
The probability of picking a white top = \(\frac{^xC1}{^{20}C1} = \frac{20}{100}\)
\(⇒ \frac{x}{20} = \frac{1}{5}\)
\(⇒ x = 4\)
Not Sufficient
If we combine the statements I and III together,
We have \(x = 4\) and total number of tops = \(20\), so the sum of number of black and grey tops = \(16\)
As the probability of both picking up is same, so \(y = z = 8\)
Hence, the data in statements I and III together is sufficient.
Hence, option C is the correct answer.
Top Questions on Probability
Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
Let \( A_1 \): People with good health,
\( A_2 \): People with average health,
and \( A_3 \): People with poor health.
During a pandemic, the data expressed that the chances of people contracting the disease from category \( A_1, A_2 \) and \( A_3 \) are 25%, 35% and 50%, respectively.
Based upon the above information, answer the following questions:
(i) A person was tested randomly. What is the probability that he/she has contracted the disease?}
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category \( A_2 \)?- If A and B are two events such that $P(B) = \frac{1}{5}$, $P(A | B) = \frac{2}{3}$ and $P(A \cup B) = \frac{3}{5}$, then $P(A)$ is :
- If \( P(A) = \frac{1}{5}, P(B) = \frac{3}{5} \) and \( P(A \cap B) = \frac{2}{5} \), then \( P(A' \cup B') \) is :
- Bag I contains 4 white and 5 black balls. Bag II contains 6 white and 7 black balls. A ball drawn randomly from Bag I is transferred to Bag II and then a ball is drawn randomly from Bag II. Find the probability that the ball drawn is white.
- A meeting will be held only if all three members A, B and C are present. The probability that member A does not turn up is 0.10, member B does not turn up is 0.20 and member C does not turn up is 0.05. The probability of the meeting being cancelled is:
Questions Asked in XAT exam
- In an 8-week course, the teacher conducts a test every week, and the scores are in the range of 1–4. There are only two students enrolled in the course, \(R\) and \(S\). The following conditions are given:
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- From the second test onwards, \(R\) consistently scored the same (a non-zero score).
- The total of the first three test scores of \(R\) equals the total of the first two test scores of \(S\).
- From the fifth test onwards, \(S\) scored the same as \(R\).
- The scores of \(S\) from the first two tests and all the remaining tests follow a geometric progression.
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