Advertisements
Advertisements
प्रश्न
Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.
Advertisements
उत्तर
When a pair of dice is rolled once, then the sample space
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4); (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Let E: 'the sum of the numbers on the dice is 4' and F: 'numbers appearing on the two dice are different'
F contains all points of 5 except (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6). This means that F contains 36 - 6 = 30 sample points
⇒ `P (F) = 30/36`
⇒ E ∩ F = {(1, 3), (3, 1)}
⇒ `P (E cap F) = 2/36`
Hence, the required probability = P (E|F)
`= (P (E cap F))/(P (F)) = (2/36)/(30/36)`
`= 2/30 = 1/15`
APPEARS IN
संबंधित प्रश्न
An insurance agent insures lives of 5 men, all of the same age and in good health. The probability that a man of this age will survive the next 30 years is known to be 2/3 . Find the probability that in the next 30 years at most 3 men will survive.
Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`
Determine P(E|F).
A coin is tossed three times, where
E: at least two heads, F: at most two heads
Determine P(E|F).
Two coins are tossed once, where
E: no tail appears, F: no head appears
A black and a red dice are rolled.
Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|F) and P (F|E)
An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple-choice question?
If P(A) = `1/2`, P(B) = 0, then P(A|B) is ______.
A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.
In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.
A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.
A card is drawn from a well-shuffled pack of playing cards. What is the probability that it is either a spade or an ace or both?
If events A and B are independent, such that `P(A)= 3/5`, `P(B)=2/3` 'find P(A ∪ B).
In a college, 70% of students pass in Physics, 75% pass in Mathematics and 10% of students fail in both. One student is chosen at random. What is the probability that:
(i) He passes in Physics and Mathematics?
(ii) He passes in Mathematics given that he passes in Physics.
(iii) He passes in Physics given that he passes in Mathematics.
A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square?
In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in subject I, if it is known that he is failed in subject II?
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, one is white and other is black?
Two balls are drawn from an urn containing 5 green, 3 blue, and 7 yellow balls one by one without replacement. What is the probability that at least one ball is blue?
Three fair coins are tossed. What is the probability of getting three heads given that at least two coins show heads?
One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are white
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events
A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays
Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?
Choose the correct alternative:
If A and B are any two events, then the probability that exactly one of them occur is
Choose the correct alternative:
If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is
Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ______
Three machines E1, E2, E3 in a certain factory produced 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.
Let A and B be two events. If P(A) = 0.2, P(B) = 0.4, P(A ∪ B) = 0.6, then P(A|B) is equal to ______.
Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to ______.
If for any two events A and B, P(A) = `4/5` and P(A ∩ B) = `7/10`, then `P(B/A)` is equal to ______.
A Problem in Mathematics is given to the three students A, B and C. Their chances of solving the problem are `1/2, 1/3` and `1/4` respectively. Find the probability that exactly two students will solve the problem.
If A and B are events and \[P(B) \neq 0\], which expression gives \[P(A \mid B)\]?
Which complement form is correct when \[P(B)\neq 0\]?
Which statement correctly describes the numerator in \[P(A\mid B)=\frac{P(A\cap B)}{P(B)}\]?
Which sequence correctly applies a given condition when finding a conditional probability?
