Advertisements
Advertisements
प्रश्न
Mark the correct alternative in the following question:
\[\text{ If A and B are such that } P\left( A \cup B \right) = \frac{5}{9} \text{ and } P\left( \overline{A} \cup \overline{B} \right) = \frac{2}{3}, \text{ then } P\left( A \right) + P\left( B \right) = \]
विकल्प
\[\frac{9}{10}\]
\[\frac{10}{9}\]
\[ \frac{8}{9} \]
\[\frac{9}{8}\]
उत्तर
\[ \text{ We have } , \]
\[P\left( A \cup B \right) = \frac{5}{9} \text{ and } P\left( \overline{A} \cup \overline{B} \right) = \frac{2}{3}\]
\[\text{ As } , P\left( \overline{A} \cup \overline{B} \right) = \frac{2}{3}\]
\[ \Rightarrow P\left( \overline{ A \cap B }\right) = \frac{2}{3}\]
\[ \Rightarrow P\left( A \cap B \right) = 1 - \frac{2}{3}\]
\[ \Rightarrow P\left( A \cap B \right) = \frac{1}{3}\]
\[ \text{ Also } , \]
\[P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) = P\left( A \cup B \right) + P\left( A \cap B \right)\]
\[ = \frac{5}{9} + \frac{1}{3}\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) = \frac{8}{9} . . . . . \left( i \right)\]
\[\text{ Now } , \]
\[P\left( \overline{A} \right) + P\left( \overline{B} \right) = 1 - P\left( A \right) + 1 - P\left( B \right)\]
\[ = 2 - \left[ P\left( A \right) + P\left( B \right) \right]\]
\[ = 2 - \frac{8}{9} \left[ \text{ Using } \left( i \right) \right]\]
\[ = \frac{10}{9}\]
APPEARS IN
संबंधित प्रश्न
A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of
(i) 5 successes?
(ii) at least 5 successes?
(iii) at most 5 successes?
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 3 white, 4 red and 5 black balls. Two balls are drawn one by one without replacement. What is the probability that at least one ball is black?
If A and B are two events such that 2 P (A) = P (B) = \[\frac{5}{13}\] and P (A/B) = \[\frac{2}{5},\] find P (A ∪ B).
A coin is tossed three times. Find P (A/B) in each of the following:
A = At most two tails, B = At least one tail.
Two coins are tossed once. Find P (A/B) in each of the following:
A = No tail appears, B = No head appears.
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?
A die is thrown twice and the sum of the numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once?
A pair of dice is thrown. Let E be the event that the sum is greater than or equal to 10 and F be the event "5 appears on the first-die". Find P (E/F). If F is the event "5 appears on at least one die", find P (E/F).
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 thrice and all the eight outcomes are assumed equally likely. In which of the following cases are the following events A and B are independent?
A = the number of heads is odd, B = the number of tails is odd.
If A and B be two events such that P (A) = 1/4, P (B) = 1/3 and P (A ∪ B) = 1/2, show that A and B are independent events.
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.
Let A and B be two independent events such that P(A) = p1 and P(B) = p2. Describe in words the events whose probabilities are: p1 + p2 - 2p1p2
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 balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that one of them is black and other is red.
A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?
A bag contains 4 white balls and 2 black balls. Another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that
(i) both are white
(ii) both are black
(iii) one is white and one is black
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?
One bag contains 4 yellow and 5 red balls. Another bag contains 6 yellow and 3 red balls. A ball is transferred from the first bag to the second bag and then a ball is drawn from the second bag. Find the probability that ball drawn is yellow.
A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.
Three machines E1, E2, E3 in a certain factory produce 50%, 25% and 25%, respectively, of the total daily output of electric bulbs. It is known that 4% of the tubes produced one each of the machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day's production, then calculate the probability that it is defective.
When three dice are thrown, write the probability of getting 4 or 5 on each of the dice simultaneously.
If A and B are two independent events such that P (A) = 0.3 and P (A ∪ \[B\]) = 0.8. Find P (B).
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 and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of Aand B occurs) = \[\frac{5}{9}\], then find the value of p.
India play two matches each with West Indies and Australia. In any match the probabilities of India getting 0,1 and 2 points are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is
A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement, 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 bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is
Choose the correct alternative in the following question:
\[\text{ If} P\left( A \right) = \frac{3}{10}, P\left( B \right) = \frac{2}{5} \text{ and } P\left( A \cup B \right) = \frac{3}{5}, \text{ then} P\left( A|B \right) + P\left( B|A \right) \text{ equals } \]
Choose the correct alternative in the following question: \[\text{ Let } P\left( A \right) = \frac{7}{13}, P\left( B \right) = \frac{9}{13} \text{ and } P\left( A \cap B \right) = \frac{4}{13} . \text{ Then } , P\left( \overline{ A }|B \right) = \]
Mark the correct alternative in the following question:
\[ \text{ If } P\left( B \right) = \frac{3}{5}, P\left( A|B \right) = \frac{1}{2} \text{ and } P\left( \overline{A \cup B }\right) = \frac{4}{5}, \text{ then } P\left( \overline{ A } \cup B \right) + P\left( A \cup B \right) = \]
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:
\[\text{ If A and B are two independent events with } P\left( A \right) = \frac{3}{5} \text{ and } P\left( B \right) = \frac{4}{9}, \text{ then } P\left( \overline{A} \cap B \right) \text{ equals } \]
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.
