Question:
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
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
Updated On: Sep 24, 2024
- 11/21
- 10/21
- 12/21
- 9/21
Hide Solution
Verified By Collegedunia
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)
Was this answer helpful?
0
0
Top Questions on Probability
- If $ A $ and $ B $ are two events such that $ P(A) = 0.7 $, $ P(B) = 0.4 $ and $ P\left( A \cap \overline{B} \right) = 0.5 $, where $\overline{B}$ denotes the complement of $ B $, then $ P\left( B | \left( A \cup \overline{B} \right) \right) $ is equal to
- JEE Main - 2025
- Mathematics
- Probability
- If the probability that the random variable X takes the value x is given by \( P(X = x) = k(x + 1)3^{-x} \), \( x = 0, 1, 2, 3, ... \), where k is a constant, then \( P(X \ge 3) \) is equal to
- JEE Main - 2025
- Mathematics
- Probability
- All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $ n $ be denoted by $ W_n $. Let the probability $ P(W_n) $ of choosing the word $ W_n $ satisfy $ P(W_n) = 2P(W_{n-1}) $, $ n>1 $. If $ P(CDBEA) = \frac{2^\alpha}{2^\beta - 1} $, $ \alpha, \beta \in \mathbb{N} $, then $ \alpha + \beta $ is equal to :
- JEE Main - 2025
- Mathematics
- Probability
- A coin is tossed and a card is selected at random from a well shuffled pack of 52 playing cards. The probability of getting head on the coin and a face card from the pack 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 :
View More Questions
Questions Asked in MAT exam
- Mohan can reach his destination on time by travelling at a speed of 54 km/hr. If one-fourth of the time, he covers \( \frac{2}{9} \) of the total distance, at what speed should the remaining distance be travelled so as to reach his destination on time?
- MAT - 2025
- Time, Speed and Distance
- Ram kumar, a trader mixes two varieties of Moong dal, totally weighing 90kg worth Rs7443. The price of the first variety that he mixes is Rs57.50 per kg and that of the second variety is Rs111.50 per kg. How much quantity of the second variety of moong dal does he mix?
- MAT - 2025
- Mixtures and Allegations
- The ages of Ajay and Vijay differ by 22.5 years. If \(6\frac{1}{2}\) years ago, Vijay was \(3\frac{1}{2}\) times as old as Ajay, find their present ages.
- MAT - 2025
- distance
- A batch of 36 school children goes for an excursion trip to Nainital. When one 10-year-old child is replaced with another child, the average age of the children in the batch increases by \( 2\frac{1}{2} \) months. What is the age of the new child?
- MAT - 2025
- Average
- A shopkeeper makes a profit of 17% by giving a discount of 22% on the marked price of an article. But with a view to gain more profit, he reduces the discount to 18% and makes a higher profit. How much is the difference in his profit percentage with this reduction in discount?
- MAT - 2025
- Profit and Loss
View More Questions