Advertisements
Advertisements
प्रश्न
There are three urns A, B, and C. Urn A contains 4 red balls and 3 black balls. urn B contains 5 red balls and 4 black balls. Urn C contains 4 red and 4 black balls. One ball is drawn from each of these urns. What is the probability that 3 balls drawn consists of 2 red balls and a black ball?
उत्तर
\[\text{ Given} :\]
\[\text{ Urn } A\left( 4R + 3B \right)\]
\[\text{ Urn } B\left( 5R + 4B \right)\]
\[\text{ Urn } C\left( 4R + 4B \right)\]
P (two red and one black ) = P ( Red from urn A ) × ( Black from urn B ) × P ( Red from urn C ) + P ( Red from urn A ) × ( Red from urn B ) × P ( Black from urn C ) + P ( Black from urn A ) × ( Red from urn B ) × P ( Red from urn C )
\[ = \frac{3}{7} \times \frac{5}{9} \times \frac{4}{8} + \frac{4}{7} \times \frac{4}{9} \times \frac{4}{8} + \frac{4}{7} \times \frac{5}{9} \times \frac{4}{8}\]
\[ = \frac{5}{42} \times \frac{16}{126} \times \frac{20}{126}\]
\[ = \frac{15 + 16 + 20}{126}\]
\[ = \frac{51}{126} = \frac{17}{42}\]
APPEARS IN
संबंधित प्रश्न
How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?
Given that the two numbers appearing on throwing two dice are different. Find the probability of the event 'the sum of numbers on the dice is 4'.
If P (A) = 0.4, P (B) = 0.3 and P (B/A) = 0.5, find P (A ∩ B) and P (A/B).
From a pack of 52 cards, two are drawn one by one without replacement. Find the probability that both of them are kings.
Find the probability that the sum of the numbers showing on two dice is 8, given that at least one die does not show five.
In a school there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that the chosen student is a girl?
A coin is tossed three times. Let the events A, B and C be defined as follows:
A = first toss is head, B = second toss is head, and C = exactly two heads are tossed in a row. B and C .
A coin is tossed three times. Let the events A, B and C be defined as follows:
A = first toss is head, B = second toss is head, and C = exactly two heads are tossed in a row. C and A
A and B are two independent events. The probability that A and B occur is 1/6 and the probability that neither of them occurs is 1/3. Find the probability of occurrence of two events.
A bag contains 3 red and 2 black balls. One ball is drawn from it at random. Its colour is noted and then it is put back in the bag. A second draw is made and the same procedure is repeated. Find the probability of drawing (i) two red balls, (ii) two black balls, (iii) first red and second black ball.
The probability that A hits a target is 1/3 and the probability that B hits it, is 2/5, What is the probability that the target will be hit, if each one of A and B shoots at the target?
The odds against a certain event are 5 to 2 and the odds in favour of another event, independent to the former are 6 to 5. Find the probability that (i) at least one of the events will occur, and (ii) none of the events will occur.
An urn contains 4 red and 7 black balls. Two balls are drawn at random with replacement. Find the probability of getting 2 red balls.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that both the balls are red.
Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.
Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal's selection is 1/3 and that of Monika's selection is 1/5. Find the probability that
(i) both of them will be selected
(ii) none of them will be selected
(iii) at least one of them will be selected
(iv) only one of them will be selected.
A bag contains 3 white, 4 red and 5 black balls. Two balls are drawn one after the other, without replacement. What is the probability that one is white and the other is black?
Tickets are numbered from 1 to 10. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of 5 and on the other a multiple of 4.
A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. What is the probability that only one of them will be selected ?
A bag contains 4 white, 7 black and 5 red balls. 4 balls are drawn with replacement. What is the probability that at least two are white?
A can hit a target 3 times in 6 shots, B : 2 times in 6 shots and C : 4 times in 4 shots. They fix a volley. What is the probability that at least 2 shots hit?
There are 3 red and 5 black balls in bag 'A'; and 2 red and 3 black balls in bag 'B'. One ball is drawn from bag 'A' and two from bag 'B'. Find the probability that out of the 3 balls drawn one is red and 2 are black.
An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting
(i) 2 red balls
(ii) 2 blue balls
(iii) One red and one blue ball.
Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among 100 students, what is the probability that: (i) you both enter the same section? (ii) you both enter the different sections?
A ordinary cube has four plane faces, one face marked 2 and another face marked 3, find the probability of getting a total of 7 in 5 throws.
If A and B are two events write the expression for the probability of occurrence of exactly one of two events.
If A, B, C are mutually exclusive and exhaustive events associated to a random experiment, then write the value of P (A) + P (B) + P (C).
If A, B and C are independent events such that P(A) = P(B) = P(C) = p, then find the probability of occurrence of at least two of A, B and C.
If A and B are independent events, then write expression for P(exactly one of A, B occurs).
A person writes 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is
A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is black or red ball is
A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is
If P (A ∪ B) = 0.8 and P (A ∩ B) = 0.3, then P \[\left( A \right)\] \[\left( A \right)\] + P \[\left( B \right)\] =
Mark the correct alternative in the following question:
\[\text{ Let A and B are two events such that } P\left( A \right) = \frac{3}{8}, P\left( B \right) = \frac{5}{8} \text{ and } P\left( A \cup B \right) = \frac{3}{4} . \text{ Then } P\left( A|B \right) \times P\left( A \cap B \right) \text{ is equals to } \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that } P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5, \text{ then } P\left( B \cap A \right) \text{ equals } \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that} P\left( A \right) \neq 0 \text{ and } P\left( B \right) \neq 1,\text{ then } P\left( \overline{ A }|\overline{ B }\right) = \]
Mark the correct alternative in the following question:
\[\text{ If the events A and B are independent, then } P\left( A \cap B \right) \text{ is equal to } \]
Mark the correct alternative in the following question:A flash light has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then the probability that both are dead is
Mark the correct alternative in the following question: A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability that exactly two of the three balls were red, the first ball being red, is
