Bissoy.com
Doctors Medicines MCQs Q&A

A bag contains black and white balls, such that the probability of picking a black ball is 4/7. If the probability of picking two black balls without replacing the first is 4/13, how many black balls are there in the bag?

A bag contains black and white balls, such that the probability of picking a black ball is 4/7. If the probability of picking two black balls without replacing the first is 4/13, how many black balls are there in the bag? Correct Answer 8

Let the bag contain ‘x’ black and ‘y’ white balls

Total no. of balls = x + y

Probability of picking a black ball = 4/7

⇒ x/(x + y) = 4/7

⇒ 7x = 4x + 4y

⇒ 3x = 4y

⇒ y = 3x/4

⇒ Total no. of balls = x + 3x/4 = 7x/4

Now, probability of picking two black balls without replacement = 4/13

⇒ × = 4/13

⇒ 4/7 × (x – 1)/(7x/4 – 1) = 4/13

⇒ 4(x – 1)/(7x – 4) = 7/13

⇒ 52(x – 1) = 7(7x – 4)

⇒ 52x – 52 = 49x – 28

⇒ 52x – 49x = 52 – 28

⇒ 3x = 24

⇒ x = 24/3 = 8

∴ There are 8 black balls in the bag

Related Questions

Compare the values of the two quantities in the question and answer. Quantity 1: A bag contains 20 balls which are red, green and blue. Find the number of red balls in the bag, if the probability of picking a blue ball is 2/5 and that of either a red or a blue ball is 3/4. Quantity 2: A bag contains 25 balls which are red, green and blue. The probability of picking a red ball first is 2/5. If the first ball was red and without keeping it back, probability of picking a blue ball is 1/3, find the number of green balls.
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: What is the probability of picking two balls, first red and second white without replacement, from a bag containing 10 red, 10 white and 5 black balls? Quantity B: What is the probability of picking first ball red, and after keeping it back, picking a second ball white, from a bag containing 10 red, 10 white and 5 black balls?
A box contains red, green, and blue colored balls, such that the probability of picking a blue ball is 37.5% of the probability of picking a red ball, and the probability of picking a red ball is 88.89% of the probability of picking a green ball. If the box contains 8 red balls, then how many total balls are there in the box?
A box contains 50 balls, in which 5 are red balls, 6 are green balls, 9 are blue balls, and the remaining are yellow balls. Quantity I: Probability of picking 2 balls such that one is green and the other one is blue Quantity II: Probability of picking 3 balls such that at least one of them is red Quantity III: Probability of picking 3 balls such that at least one of them is blue
Each of the question below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. A bag contains some number of Diamond of 4 different colors (Red, Pink, blue and yellow). What is the total number of Diamond in the bag? I. If 5 Pink Diamond from the bag are replaced by Yellow Diamond, Then the ratio of probabilities of picking 2 yellow Diamond at a time to picking 3 Blue Diamond at a time becomes (1/116). II. The different between probabilities of picking 2 Red Diamonds at a time and probability of picking 2 Blue Diamonds at a time is (23/330). III. If a Diamond is picked from the bag, then there is 40% chance that it is a red Diamond. Probability of picking 2 Red Diamond from the bag is (26/165).
Ashutosh has a box containing 8 identical red balls, 9 identical blue balls and 10 identical green balls. He is required to distribute all these balls into three bags A, B and C such that the total number of balls in bag A is more than that in bag B, which, in turn, is more than that in bag C. Moreover, he needs to ensure that the number or red balls in bag A is more than that in bag B which in turn is more than that in bag C, and similarly for the blue and green balls. In how many ways can he do this? Each bag must contain at least one ball of each type.
A box contains black and white balls, such that the probability of picking a black ball is 3/11. When 8 more black balls are added to the box, the probability of picking a black ball becomes 5/13. Find the number of white balls in the box.
The following question, there are three statements I, II and III. Read the question carefully and mark your answer according to which statements(s) is/are sufficient to the answer the question. Find the probability that both the balls are of blue color. Statement I: In a bag containing 4 red balls, 6 blue balls and 8 yellow balls, two balls are drawn at random one by one without replacement. Statement II: First ball is blue and if this happens then 5 more blue balls are added in the bag Statement III: Total blue balls are twice more than the other balls at the end of the drawing of balls
A box contains balls of two colours, black and white. A total of 28 balls were taken out from the box constituting of 1/5 of the black balls and 1/10 of the white balls. When 3/4 of the remaining black balls and 2/3 of the remaining white balls were also taken out, only 50 balls were left in the box. How many total balls were initially there in the box?
একটি থলেতে 4 টি সাদা এবং 2 টি কালো বল আছে। অপর একটি থলেতে 3 টি সাদা ও 5 টি কালো বল আছে। যদি প্রত্যেক থলে হতে একটি করে বল উত্তোলন করা হয়, তবে বলদ্বয় সাদা হওয়ার সম্ভাবনা কত? (A bag contains 4 white and 2 black balls. Another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, what is the probability that both balls are white?)