Advertisements
Advertisements
प्रश्न
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.
उत्तर
\[P\left( A \right) = P\left( 4, 5 \text { or }6 \text{ on first toss } \right) = \frac{18}{36} = \frac{1}{2}\]
\[P\left( B \right) = P\left( 1, 2, 3 \text { or } 4 \text{ on second toss } \right) = \frac{24}{36} = \frac{2}{3}\]
\[\text{ It is clear that A and B are independent events.} \]
\[ \Rightarrow P\left( A \cap B \right) = P\left( A \right)P\left( B \right)\]
\[ \Rightarrow P\left( A \cap B \right) = \frac{1}{2} \times \frac{2}{3}\]
\[ \therefore P\left( A \cap B \right) = \frac{1}{3}\]
APPEARS IN
संबंधित प्रश्न
A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins
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).
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?
A bag contains 4 white, 7 black and 5 red balls. Three balls are drawn one after the other without replacement. Find the probability that the balls drawn are white, black and red respectively.
If A and B are events such that P (A) = 0.6, P (B) = 0.3 and P (A ∩ B) = 0.2, find P (A/B) and P (B/A).
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.
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.
In a school there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that the chosen student is a girl?
Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?
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.
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 odd, B = the number of tails is odd.
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 (A ∩ overlineB ) `.
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find \[P \overline A \cup \overline B \] .
If A and B are two independent events such that P (`bar A` ∩ B) = 2/15 and P (A ∩`bar B` ) = 1/6, then find P (B).
A die is tossed twice. Find the probability of getting a number greater than 3 on each toss.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red, (ii) first ball is black and second is red, (iii) one of them is black and other is red.
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 .
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.
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?
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 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.
Three persons A, B, C throw a die in succession till one gets a 'six' and wins the game. Find their respective probabilities of winning.
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.
Two dice are thrown simultaneously. The probability of getting a pair of aces 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
If P (A ∪ B) = 0.8 and P (A ∩ B) = 0.3, then P \[\left( A \right)\] \[\left( A \right)\] + P \[\left( B \right)\] =
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:
\[\text{ If} P\left( A \right) = \frac{3}{10}, P\left( B \right) = \frac{2}{5} \text{ and } P\left( A \cup B \right) = \frac{3}{5}, \text{ then} P\left( A|B \right) + P\left( B|A \right) \text{ equals } \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that } P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3}, P\left( A|B \right) = \frac{1}{4}, \text{ then } P\left( A \cap B \right) \text{ equals} \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two independent events with } P\left( A \right) = \frac{3}{5} \text{ and } P\left( B \right) = \frac{4}{9}, \text{ then } P\left( \overline{A} \cap B \right) \text{ equals } \]
Mark the correct alternative in the following question:
\[\text{ If A and B are two independent events such that} P\left( A \right) = 0 . 3 \text{ and } P\left( A \cup B \right) = 0 . 5, \text{ then } P\left( A|B \right) - P\left( B|A \right) = \]
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
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).
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.
