There are two bags, one of which contains 3 black and 4 white balls, while the other contains 4 black and 3 white balls. A dice is cast.If the face 1 or 3 turns up, a ball is taken from the first bag and if any other face turns up a ball is chosen from the second bag. The probability of choosing a black ball is
- 11/21
- 10/21
- 12/21
- 9/21
The Correct Option is A
Solution and Explanation
Bag1 = 3 back, 4 white balls
Bag2 = 4 black, 3 white balls
Probability of selecting bag 1 \(=\frac{2}{6}=\frac{1}{3}\)
Probability of selecting bag 2 \(=1-\frac{1}{3}=\frac{2}{3}\)
Probability of choosing a black ball from bag 1 \(=\frac{3}{7}\)
Probability of choosing a black ball from bag 2 \(=\frac{4}{7}\)
Required probability \(=\frac{1}{3}\times\frac{3}{7}+\frac{2}{3}\times\frac{4}{7}\)
\(=\frac{11}{21}\).So the correct option is (A)
Top Questions on Probability
- A bag contains 3 red and 2 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
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 :
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- 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.
Questions Asked in MAT exam
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- 24% of all items were blankets.
- $\frac{1}{6}$ of all items were jackets.
- 14% of all items were shoes.
- Remaining items were either socks or room heaters.
- The number of room heaters distributed was 100 more than the number of socks distributed.
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- Data Analysis
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- 24% of all items were blankets.
- $\frac{1}{6}$ of all items were jackets.
- 14% of all items were shoes.
- Remaining items were either socks or room heaters.
- The number of room heaters distributed was 100 more than the number of socks distributed.
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- Data Analysis
- An international NGO for homeless people has supplied certain items for ongoing winters to new shelters for homeless people. These consist of different items like blankets, jackets, shoes, socks, and room heaters. The total number of five items distributed in December 2024 was 3300.
- 24% of all items were blankets.
- $\frac{1}{6}$ of all items were jackets.
- 14% of all items were shoes.
- Remaining items were either socks or room heaters.
- The number of room heaters distributed was 100 more than the number of socks distributed.
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1. The family consists of 3 married couples and each couple forms a group.
2. The oldest member of the family goes to Canada.
3. H, a female, is married to E, who does not go to UK.
4. B and Dform a group and agreed to go to USA.
5. E’s mother-in-law is the mother of C, who is the father of B and brother of H.
6. A is the grandfather of one of the male members, who goes to USA.
7. D is unmarried and the niece of C.
8. F is the oldest member of the family.
Which of the following members will go to Canada?- MAT - 2025
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- An international NGO for homeless people has supplied certain items for ongoing winters to new shelters for homeless people. These consist of different items like blankets, jackets, shoes, socks, and room heaters. The total number of five items distributed in December 2024 was 3300.
- 24% of all items were blankets.
- $\frac{1}{6}$ of all items were jackets.
- 14% of all items were shoes.
- Remaining items were either socks or room heaters.
- The number of room heaters distributed was 100 more than the number of socks distributed.
What is the difference between the total number of socks and blankets distributed and the number of shoes distributed?- MAT - 2025
- Data Analysis