Advertisements
Advertisements
प्रश्न
Mark the correct alternative in the following question:
A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number of the die and a spade card is
पर्याय
\[ \frac{1}{2} \]
\[ \frac{1}{4} \]
\[\frac{1}{8}\]
\[ \frac{3}{4}\]
उत्तर
\[\text{ Let } : \]
\[\text{ A be the event of getting an even number of the die and } \]
\[ \text{ B be the event of getting a spade card } \]
\[\text{ Now } , \]
\[P\left( \text{ getting an even number of the die and a spade card } \right) = P\left( AB \right)\]
\[ = P\left( A \right) \times P\left( B|A \right)\]
\[ = \frac{3}{6} \times \frac{13}{52}\]
\[ = \frac{1}{8}\]
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%?
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 P (A) = 0.4, P (B) = 0.3 and P (B/A) = 0.5, find P (A ∩ B) and P (A/B).
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 25 tickets, numbered from 1 to 25. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show even numbers.
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 card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. Find the probability that the first card is a heart and the second card is a diamond if the first card is not replaced.
Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and third card drawn is an ace?
If A and B are two events such that \[ P\left( A \right) = \frac{7}{13}, P\left( B \right) = \frac{9}{13} \text{ and } P\left( A \cap B \right) = \frac{4}{13}, \text{ then find } P\left( \overline{ A }|B \right) . \]
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 = 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.
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 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?
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 (A ∪ B).
If P (not B) = 0.65, P (A ∪ B) = 0.85, and A and B are independent events, then find P (A).
Three cards are drawn with replacement from a well shuffled pack of cards. Find the probability that the cards drawn are king, queen and jack.
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?
An urn contains 4 red and 7 black balls. Two balls are drawn at random with replacement. Find the probability of getting 2 blue balls.
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 first ball is black and second is red.
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 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 card is drawn from a well-shuffled deck of 52 cards. The outcome is noted, the card is replaced and the deck reshuffled. Another card is then drawn from the deck.
(i) What is the probability that both the cards are of the same suit?
(ii) What is the probability that the first card is an ace and the second card is a red queen?
A bag contains 6 red and 8 black balls and another bag contains 8 red and 6 black balls. A ball is drawn from the first bag and without noticing its colour is put in the second bag. A ball is drawn from the second bag. Find the probability that the ball drawn is red in colour.
A four digit number is formed using the digits 1, 2, 3, 5 with no repetitions. Write the probability that the number is divisible by 5.
If A and B are two events write the expression for the probability of occurrence of exactly one of two events.
Write the probability that a number selected at random from the set of first 100 natural numbers is a cube.
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
Three integers are chosen at random from the first 20 integers. The probability that their product is even is
Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, 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
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:A flash light has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then the probability that both are dead is
Mark the correct alternative in the following question:
\[\text{ Let A and B be two events such that P } \left( A \right) = 0 . 6, P\left( B \right) = 0 . 2, P\left( A|B \right) = 0 . 5 . \text{ Then } P\left( \overline{A}|\overline{B} \right) \text{ equals } \]
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.
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.
