Advertisements
Advertisements
प्रश्न
Compute P (A/B), if P (B) = 0.5 and P (A ∩ B) = 0.32
उत्तर
\[\text{ Given } : \]
\[P\left( B \right) = 0 . 5\]
\[P\left( A \cap B \right) = 0 . 32\]
\[\text{ Now } , \]
\[ P\left( \frac{A}{B} \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)}\]
\[ \Rightarrow P\left( \frac{A}{B} \right) = \frac{0 . 32}{0 . 5} = \frac{32}{50} = \frac{16}{25}\]
APPEARS IN
संबंधित प्रश्न
A die is thrown three times, find the probability that 4 appears on the third toss if it is given that 6 and 5 appear respectively on first two tosses.
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that the first is a king and the second is an ace.
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 \[ P\left( A \right) = \frac{1}{3}, P\left( B \right) = \frac{1}{4} \text{ and } P\left( A \cup B \right) = \frac{5}{12}, \text{ then find } P\left( A|B \right) \text{ and } P\left( B|A \right) . \]
Two coins are tossed once. Find P (A/B) in each of the following:
A = Tail appears on one coin, B = One coin shows head.
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 a prime number.
A die is rolled. If the outcome is an odd number, what is the probability that it is prime?
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.
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 first throw results in head, B = the last throw results in tail.
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.
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find \[P \overline A \cup \overline B \] .
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (A ∪ B).
An anti-aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?
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 .
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 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?
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.
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.
A, B, and C are independent witness of an event which is known to have occurred. Aspeaks the truth three times out of four, B four times out of five and C five times out of six. What is the probability that the occurrence will be reported truthfully by majority of three witnesses?
A and B take turns in throwing two dice, the first to throw 9 being awarded the prize. Show that their chance of winning are in the ratio 9:8.
Fatima and John appear in an interview for two vacancies for the same post. The probability of Fatima's selection is \[\frac{1}{7}\] and that of John's selection is \[\frac{1}{5}\] What is the probability that
(i) both of them will be selected?
(ii) only one of them will be selected?
(iii) none of them will be selected?
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 bag A contains 5 white and 6 black balls. Another bag B contains 4 white and 3 black balls. A ball is transferred from bag A to the bag B and then a ball is taken out of the second bag. Find the probability of this ball being black.
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.
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, B, C are mutually exclusive and exhaustive events associated to a random experiment, then write the value of P (A) + P (B) + P (C).
A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is
The probabilities of a student getting I, II and III division in an examination are \[\frac{1}{10}, \frac{3}{5}\text{ and } \frac{1}{4}\]respectively. The probability that the student fails in the examination is
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
Choose the correct alternative in the following question:
If A and B are two events associated to a random experiment such that \[P\left( A \cap B \right) = \frac{7}{10} \text{ and } P\left( B \right) = \frac{17}{20}\] , then P(A|B) =
Mark the correct alternative in the following question:
\[\text{ If} P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 8 \text{ and } P\left( B|A \right) = 0 . 6, \text{ then } P\left( A \cup B \right) = \]
Mark the correct alternative in the following question:
\[\text{ If } P\left( B \right) = \frac{3}{5}, P\left( A|B \right) = \frac{1}{2} \text{ and } P\left( A \cup B \right) = \frac{4}{5}, \text{ then } P\left( B|\overline{ A } \right) = \]
Mark the correct alternative in the following question:
Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability that both cards are queen is
Mark the correct alternative in the following question:
A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is
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 ______.
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.
