Advertisements
Advertisements
प्रश्न
If S is the sample space and P (A) = \[\frac{1}{3}\]P (B) and S = A ∪ B, where A and B are two mutually exclusive events, then P (A) =
विकल्प
1/4
1/2
3/4
3/8
उत्तर
\[\frac{1}{4}\]
\[P\left( A \right) = \frac{1}{3}P\left( B \right)\]
\[ \Rightarrow P\left( B \right) = 3P\left( A \right) . . . \left( 1 \right)\]
\[\text{ A and B are mutually exclusive events } .\]
\[\Rightarrow P\left( A \cap B \right) = 0\]
\[\text{ Now } ,\]
\[P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) = P\left( S \right)\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) = 1\]
\[ \Rightarrow P\left( A \right) + 3P\left( A \right) = 1 \left[ \text{ From } \left( 1 \right) \right]\]
\[ \Rightarrow 4P\left( A \right) = 1\]
\[ \Rightarrow P\left( A \right) = \frac{1}{4}\]
APPEARS IN
संबंधित प्रश्न
From a deck of cards, three cards are drawn on by one without replacement. Find the probability that each time it is a card of spade.
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that the first is a heart and second is red.
A bag contains 20 tickets, numbered from 1 to 20. Two tickets are drawn without replacement. What is the probability that the first ticket has an even number and the second an odd number.
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 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 = Heads on third toss, B = Heads on first two tosses.
Two coins are tossed once. Find P (A/B) in each of the following:
A = No tail appears, B = No head appears.
A pair of dice is thrown. Find the probability of getting 7 as the sum, if it is known that the second die always exhibits an odd number.
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.
Check the independence of A and B.
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.
An article manufactured by a company consists of two parts X and Y. In the process of manufacture of the part X, 9 out of 100 parts may be defective. Similarly, 5 out of 100 are likely to be defective in the manufacture of part Y. Calculate the probability that the assembled product will not be defective.
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.
Arun and Tarun appeared for an interview for two vacancies. The probability of Arun's selection is 1/4 and that to Tarun's rejection is 2/3. Find the probability that at least one of them will be selected.
In a family, the husband tells a lie in 30% cases and the wife in 35% cases. Find the probability that both contradict each other on the same fact.
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 none of them will be selected?
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
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?
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.
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.
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.
The contents of three bags I, II and III are as follows:
Bag I : 1 white, 2 black and 3 red balls,
Bag II : 2 white, 1 black and 1 red ball;
Bag III : 4 white, 5 black and 3 red balls.
A bag is chosen at random and two balls are drawn. What is the probability that the balls are white and red?
An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the sum of the numbers obtained is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4, ..., 12 is picked and the number on the card is noted. What is the probability that the noted number is either 7 or 8?
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 and B are two independent events, then write P (A ∩ \[B\] ) in terms of P (A) and P (B).
A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is
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
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
Choose the correct alternative in the following question:
Associated to a random experiment two events A and B are such that
Choose the correct alternative in the following question:
\[\text{ If } P\left( A \right) = \frac{2}{5}, P\left( B \right) = \frac{3}{10} \text{ and } P\left( A \cap B \right) = \frac{1}{5}, \text{ then } , P\left( \overline { A }|\overline{ B } \right) P\left( \overline{ B }|\overline{ A } \right) \text{ is equal to } \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that } P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5, \text{ then } P\left( B \cap A \right) \text{ equals } \]
Mark the correct alternative in the following question: A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability of getting exactly one red ball is
Mark the correct alternative in the following question:
In a college 30% students fail in Physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in Physics if she failed in Mathematics is
Mark the correct alternative in the following question:
If two events are independent, then
Mark the correct alternative in the following question:
Two dice are thrown. If it is known that the sum of the numbers on the dice was less than 6, then the probability of getting a sum 3, 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).
An insurance company insured 3000 cyclists, 6000 scooter drivers, and 9000 car drivers. The probability of an accident involving a cyclist, a scooter driver, and a car driver are 0⋅3, 0⋅05 and 0⋅02 respectively. One of the insured persons meets with an accident. What is the probability that he is a cyclist?
Refer to Question 6. Calculate the probability that the defective tube was produced on machine E1.
