Advertisements
Advertisements
प्रश्न
An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is
विकल्प
\[\frac{5}{84}\]
\[\frac{3}{9}\]
\[\frac{3}{7}\]
\[\frac{7}{17}\]
उत्तर
\[ \frac{5}{84}\]
\[\text{ Given }: \]
\[\text{ Red balls} = 2\]
\[\text{ Blue balls} = 3\]
\[\text{ Black balls } = 4\]
\[P\left( \text{ all three balls are of same colour } \right) = P(\text{ all three are blue } ) + P\left( \text{ all three are black } \right)\]
\[ = \frac{3}{9} \times \frac{2}{8} \times \frac{1}{7} + \frac{4}{9} \times \frac{3}{8} \times \frac{2}{7}\]
\[ = \frac{1}{84} + \frac{4}{84}\]
\[ = \frac{5}{84}\]
APPEARS IN
संबंधित प्रश्न
If A and B are two events such that P (A) = \[\frac{1}{3},\] P (B) = \[\frac{1}{5}\] and P (A ∪ B) = \[\frac{11}{30}\] , find P (A/B) and P (B/A).
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that both are kings .
An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?
If A and B are two events such that\[ P\left( A \right) = \frac{6}{11}, P\left( B \right) = \frac{5}{11} \text{ and } P\left( A \cup B \right) = \frac{7}{11}, \text{ then find } P\left( A \cap B \right), P\left( A|B \right) \text { and } P\left( B|A \right) . \]
If A and B are two events such that
\[ P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3} \text{ and } P\left( A \cap B \right) = \frac{1}{4}, \text{ then find } P\left( A|B \right), P\left( B|A \right), P\left( \overline{ A }|B \right) \text{ and } P\left( \overline{ A }|\overline{ B } \right) .\]
If P (A) = \[\frac{6}{11},\] P (B) = \[\frac{5}{11}\] and P (A ∪ B) = \[\frac{7}{11},\] find
A die is thrown three times. Find P (A/B) and P (B/A), if
A = 4 appears on the third toss, B = 6 and 5 appear respectively on first two tosses.
A dice is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (B/A) .
If P (not B) = 0.65, P (A ∪ B) = 0.85, and A and B are independent events, then find P (A).
An unbiased die is tossed twice. Find the probability of getting 4, 5, or 6 on the first toss and 1, 2, 3 or 4 on the second toss.
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.
A bag contains 6 black and 3 white balls. Another bag contains 5 black and 4 white balls. If one ball is drawn from each bag, find the probability that these two balls are of the same colour.
A bag contains 7 white, 5 black and 4 red balls. Four balls are drawn without replacement. Find the probability that at least three balls are black.
Three cards are drawn with replacement from a well shuffled pack of 52 cards. Find the probability that the cards are a king, a queen and a jack.
A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its colour is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be
(i) blue followed by red.
(ii) blue and red in any order.
(iii) of the same colour.
A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.
A bag contains 4 white and 5 black balls and another bag contains 3 white and 4 black balls. A ball is taken out from the first bag and without seeing its colour is put in the second bag. A ball is taken out from the latter. Find the probability that the ball drawn is white.
Three digit numbers are formed with the digits 0, 2, 4, 6 and 8. Write the probability of forming a three digit number with the same digits.
An unbiased die with face marked 1, 2, 3, 4, 5, 6 is rolled four times. Out of 4 face values obtained, find the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5.
Write the probability that a number selected at random from the set of first 100 natural numbers is a cube.
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.
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 coin is tossed three times. If events A and B are defined as A = Two heads come, B = Last should be head. Then, A and B are ______.
A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour 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:
\[\text{ If A and B are two events such that} P\left( A \right) \neq 0 \text{ and } P\left( B \right) \neq 1,\text{ then } P\left( \overline{ A }|\overline{ B }\right) = \]
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:
\[\text{ If A and B are two events such that } P\left( A|B \right) = p, P\left( A \right) = p, P\left( B \right) = \frac{1}{3} \text{ and } P\left( A \cup B \right) = \frac{5}{9}, \text{ then} p = \]
If two events A and B are such that P (A)
\[\left( \overline{ A } \right)\] = 0.3, P (B) = 0.4 and P (A ∩ B) = 0.5, find P \[\left( B/\overline{ A }\cap \overline{ B } \right)\].
The probability that in a year of 22nd century chosen at random, there will be 53 Sunday, is ______.
Mother, father and son line up at random for a family photo. If A and B are two events given by
A = Son on one end, B = Father in the middle, find P(B / A).
A, B and C throw a pair of dice in that order alternatively till one of them gets a total of 9 and wins the game. Find their respective probabilities of winning, if A starts first.
A and B throw a die alternately till one of them gets a '6' and wins the game. Find their respective probabilities of winning, if A starts the game first.
