Advertisements
Advertisements
प्रश्न
If P (A) = 0.4, P (B) = 0.3 and P (B/A) = 0.5, find P (A ∩ B) and P (A/B).
उत्तर
\[\text{ Given } : \]
\[P\left( A \right) = 0 . 4\]
\[P\left( B \right) = 0 . 3\]
\[P\left( B/A \right) = 0 . 5\]
\[\text{ Now } , \]
\[P\left( B/A \right) = \frac{P\left( A \cap B \right)}{P\left( A \right)}\]
\[ \Rightarrow 0 . 5 = \frac{P\left( A \cap B \right)}{0 . 4}\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 2\]
\[\]
\[P\left( A/B \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)} = \frac{0 . 2}{0 . 3} = \frac{2}{3}\]
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%?
Bag A contains 3 red and 5 black balls, while bag B contains 4 red and 4 black balls. Two balls are transferred at random from bag A to bag B and then a ball is drawn from bag B at random. If the ball drawn from bag B is found to be red find the probability that two red balls were transferred from A to B.
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).
From a pack of 52 cards, 4 are drawn one by one without replacement. Find the probability that all are aces(or kings).
A bag contains 5 white, 7 red and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.
If A and B are two events such that \[ P\left( A \right) = \frac{7}{13}, P\left( B \right) = \frac{9}{13} \text{ and } P\left( A \cap B \right) = \frac{4}{13}, \text{ then find } P\left( \overline{ A }|B \right) . \]
If A and B are two events such that
\[ P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3} \text{ and } P\left( A \cap B \right) = \frac{1}{4}, \text{ then find } P\left( A|B \right), P\left( B|A \right), P\left( \overline{ A }|B \right) \text{ and } P\left( \overline{ A }|\overline{ B } \right) .\]
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.
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.
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 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.
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.
Two numbers are selected at random from integers 1 through 9. If the sum is even, find the probability that both the numbers are odd.
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 two, B = the last throw results in head.
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (A ∩ B).
Given two independent events A and B such that P (A) = 0.3 and P (B) `= 0.6. Find P ( overlineA ∩ B) .`
Given the probability that A can solve a problem is 2/3 and the probability that B can solve the same problem is 3/5. Find the probability that none of the two will be able to solve the problem.
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?
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 .
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 cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.
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?
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 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 bag contains 4 red and 5 black balls, a second bag contains 3 red and 7 black balls. One ball is drawn at random from each bag, find the probability that the (i) balls are of different colours (ii) balls are 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.
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.
One bag contains 4 white and 5 black balls. Another bag contains 6 white and 7 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is white.
If A and B are two independent events, then write P (A ∩ \[B\] ) in terms of P (A) and P (B).
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 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
Three integers are chosen at random from the first 20 integers. The probability that their product is even 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) =
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:
\[\text{ If A and B are two independent events with } P\left( A \right) = \frac{3}{5} \text{ and } P\left( B \right) = \frac{4}{9}, \text{ then } P\left( \overline{A} \cap B \right) \text{ equals } \]
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.
