Advertisements
Advertisements
प्रश्न
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.
उत्तर
Consider the given events.
A = A heart in the first throw
B = A red card in the second throw
\[\text{ Now } , \]
\[P\left( A \right) = \frac{13}{52} = \frac{1}{4}\]
\[P\left( B/A \right) = \frac{25}{51}\]
\[ \therefore \text{ Required probability } = P\left( A \cap B \right)\]
\[ = P\left( A \right) \times P\left( B/A \right)\]
\[ = \frac{1}{4} \times \frac{25}{51}\]
\[ = \frac{25}{204}\]
APPEARS IN
संबंधित प्रश्न
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.
Compute P (A/B), if P (B) = 0.5 and P (A ∩ B) = 0.32
If P (A) = 0.4, P (B) = 0.3 and P (B/A) = 0.5, find P (A ∩ B) and P (A/B).
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
\[ P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3} \text{ and } P\left( A \cap B \right) = \frac{1}{4}, \text{ then find } P\left( A|B \right), P\left( B|A \right), P\left( \overline{ A }|B \right) \text{ and } P\left( \overline{ A }|\overline{ B } \right) .\]
If P (A) = \[\frac{6}{11},\] P (B) = \[\frac{5}{11}\] and P (A ∪ B) = \[\frac{7}{11},\] find
A coin is tossed three times. Find P (A/B) in each of the following:
A = At least two heads, B = At most two heads
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.
Mother, father and son line up at random for a family picture. If A and B are two events given by A = Son on one end, B = Father in the middle, find P (A/B) and P (B/A).
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 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 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.
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. B and C .
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.
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.
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.
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?
Two dice are thrown together and the total score is noted. The event E, F and G are "a total of 4", "a total of 9 or more", and "a total divisible by 5", respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.
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
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?
The probability of student A passing an examination is 2/9 and of student B passing is 5/9. Assuming the two events : 'A passes', 'B passes' as independent, find the probability of : (i) only A passing the examination (ii) only one of them passing the examination.
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?
Three numbers are chosen from 1 to 20. Find the probability that they are consecutive.
If A and B are two independent events, then write P (A ∩ \[B\] ) in terms of P (A) and P (B).
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
A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is
Choose the correct alternative in the following question:
Associated to a random experiment two events A and B are such that
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:
\[\text{ If A and B are two events such that } P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5, \text{ then } P\left( B \cap A \right) \text{ equals } \]
If A and B are two events such that A ≠ Φ, B = Φ, then
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 that exactly two of the three balls were red, the first ball being red, 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
Mark the correct alternative in the following question:
If two events are independent, then
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.
