Advertisements
Advertisements
प्रश्न
A speaks the truth 8 times out of 10 times. A die is tossed. He reports that it was 5. What is the probability that it was actually 5?
Advertisements
उत्तर
Let A denote the event that man reports that 5 occurs and E the event that 5 actually turns up.
∴ P(E) = \[\frac{1}{6}\] \[P\left( \overline{ E } \right) = 1 - \frac{1}{6} = \frac{5}{6}\]
Also,
APPEARS IN
संबंधित प्रश्न
In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4 What is the probability that the student knows the answer given that he answered it correctly?
Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?
Probability that A speaks truth is `4/5` . A coin is tossed. A reports that a head appears. The probability that actually there was head is ______.
If A and B are two events such that A ⊂ B and P (B) ≠ 0, then which of the following is correct?
Of the students in a school, it is known that 30% have 100% attendance and 70% students are irregular. Previous year results report that 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination. At the end of the year, one student is chos~n at random from the school and he was found ·to have an A grade. What is the probability that the student has 100% attendance? Is regularity required only in school? Justify your answer
A speaks the truth 8 times out of 10 times. A die is tossed. He reports that it was 5. What is the probability that it was actually 5?
A letter is known to have come either from LONDON or CLIFTON. On the envelope just two consecutive letters ON are visible. What is the probability that the letter has come from
(i) LONDON (ii) CLIFTON?
An insurance company insured 3000 scooters, 4000 cars and 5000 trucks. The probabilities of the accident involving a scooter, a car and a truck are 0.02, 0.03 and 0.04 respectively. One of the insured vehicles meet with an accident. Find the probability that it is a (i) scooter (ii) car (iii) truck.
A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, whereas the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B on the job for 30% of the time and C on the job for 20% of the time. A defective item is produced. What is the probability that it was produced by A?
An insurance company insured 2000 scooters and 3000 motorcycles. The probability of an accident involving a scooter is 0.01 and that of a motorcycle is 0.02. An insured vehicle met with an accident. Find the probability that the accidented vehicle was a motorcycle.
There are three coins. One is two-headed coin (having head on both faces), another is biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tail 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin?
A company has two plants to manufacture bicycles. The first plant manufactures 60% of the bicycles and the second plant 40%. Out of the 80% of the bicycles are rated of standard quality at the first plant and 90% of standard quality at the second plant. A bicycle is picked up at random and found to be standard quality. Find the probability that it comes from the second plant.
For A, B and C the chances of being selected as the manager of a firm are in the ratio 4:1:2 respectively. The respective probabilities for them to introduce a radical change in marketing strategy are 0.3, 0.8 and 0.5. If the change does take place, find the probability that it is due to the appointment of B or C.
There are three coins. One is two headed coin, another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin?
Let d1, d2, d3 be three mutually exclusive diseases. Let S be the set of observable symptoms of these diseases. A doctor has the following information from a random sample of 5000 patients: 1800 had disease d1, 2100 has disease d2 and the others had disease d3. 1500 patients with disease d1, 1200 patients with disease d2 and 900 patients with disease d3 showed the symptom. Which of the diseases is the patient most likely to have?
A test for detection of a particular disease is not fool proof. The test will correctly detect the disease 90% of the time, but will incorrectly detect the disease 1% of the time. For a large population of which an estimated 0.2% have the disease, a person is selected at random, given the test, and told that he has the disease. What are the chances that the person actually have the disease?
There are three bags, each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles and Bag 3 has 45 red and 55 blue marbles. One of the bags is chosen at random and a marble is picked from the chosen bag. What is the probability that the chosen marble is red?
If E1 and E2 are equally likely, mutually exclusive and exhaustive events and `"P"("A"/"E"_1 )` = 0.2, `"P"("A"/"E"_2)` = 0.3. Find `"P"("E"_1/"A")`
Solve the following:
The chances of P, Q and R, getting selected as principal of a college are `2/5, 2/5, 1/5` respectively. Their chances of introducing IT in the college are `1/2, 1/3, 1/4` respectively. Find the probability that IT is introduced by Q
Solve the following:
Given three identical boxes, I, II, and III, each containing two coins. In box I, both coins are gold coins, in box II, both are silver coins and in box III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold?
Solve the following:
In a factory which manufactures bulbs, machines A, B and C manufacture respectively 25%, 35% and 40% of the bulbs. Of their outputs, 5, 4 and 2 percent are respectively defective bulbs. A bulbs is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B?
There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it. if the ball is black, what is the probability that it is from the first urn?
The chances of A, B and C becoming manager of a certain company are 5 : 3 : 2. The probabilities that the office canteen will be improved if A, B, and C become managers are 0.4, 0.5 and 0.3 respectively. If the office canteen has been improved, what is the probability that B was appointed as the manager?
Suppose that 6% of the people with blood group O are left handed and 10% of those with other blood groups are left handed 30% of the people have blood group O. If a left handed person is selected at random, what is the probability that he/she will have blood group O?
Refer to Question 41 above. If a white ball is selected, what is the probability that it came from Bag 2
Refer to Question 41 above. If a white ball is selected, what is the probability that it came from Bag 3
In a bolt factory, machines X, Y and Z manufacture 20%, 35% and 45% respectively of the total output. Of their output 8%, 6% and 5% respectively are defective bolts. One bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured in machine Y?
| CASE-BASED/DATA-BASED |
![]() |
| An insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. The company’s statistics show that an accident-prone person will have an accident at some time within a fixed one-year period with a probability 0.6, whereas this probability is 0.2 for a person who is not accident prone. The company knows that 20 percent of the population is accident prone. |
Based on the given information, answer the following questions.
- What is the probability that a new policyholder will have an accident within a year of purchasing a policy?
- Suppose that a new policyholder has an accident within a year of purchasing a policy. What is the probability that he or she is accident prone?
Probability that 'A' speaks truth is `4/5`. A coin is taked. A reports that head appears. the probability that actually there was head is
If 'A' and 'B' are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is true :-
In a factory, machine A produces 30% of total output, machine B produces 25% and the machine C produces the remaining output. The defective items produced by machines A, B and C are 1%,1.2%, 2% respectively. An item is picked at random from a day's output and found to be defective. Find the probability that it was produced by machine B?
A speaks truth in 75% of the cases and B in 80% of the cases. The percentage of cases they are likely to contradict each other in making the same statement is ______.
Why is Bayes' Theorem often called a method of finding reverse probability?
Which conditions must hold for \[B_1, B_2, \dots, B_n\] in Bayes' Theorem?
Which formula represents the Law of Total Probability?

