Advertisements
Advertisements
प्रश्न
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 in the college after one of them is selected as a principal
Advertisements
उत्तर
Let event P: P become principal.
event Q: Q become principal.
event R: R become principal.
event E: Subject IT is introduced.
Given, `"P"("P") = 2/5, "P"("Q") = 2/5, "P"("R") = 1/5`
and `"P"("E"/"P") = 1/2, "P"("E"/"Q") = 1/3`,
`"P"("E"/"R") = 1/4`
Required probability = P(E)
= `"P"("P") * "P"("E"/"P") + "P"("Q") * "P"("E"/"Q") + "P"("R") * "P"("E"/"R")`
= `2/5 xx 1/2 + 2/5 xx 1/3 + 1/5 xx 1/4`
= `1/5 + 2/15 + 1/20`
= `(12 + 8 + 3)/60`
= `23/60`
APPEARS IN
संबंधित प्रश्न
There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the times and the third is also a biased coin that comes up tails 40% of the time. 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 bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as 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 is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that was produced by A?
A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.
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 ______.
Three machines E1, E2 and E3 in a certain factory producing electric bulbs, produce 50%, 25% and 25% respectively, of the total daily output of electric bulbs. It is known that 4% of the bulbs produced by each of machines E1 and E2are defective and that 5% of those produced by machine E3 are defective. If one bulb is picked up at random from a day's production, calculate the probability that it is defective.
An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident for them are 0.01, 0.03 and 0.15, respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver or a car driver?
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?
The contents of urns I, II, III are as follows:
Urn I : 1 white, 2 black and 3 red balls
Urn II : 2 white, 1 black and 1 red balls
Urn III : 4 white, 5 black and 3 red balls.
One urn is chosen at random and two balls are drawn. They happen to be white and red. What is the probability that they come from Urns I, II, III?
A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag B.
Three urns contains 2 white and 3 black balls; 3 white and 2 black balls and 4 white and 1 black ball respectively. One ball is drawn from an urn chosen at random and it was found to be white. Find the probability that it was drawn from the first urn.
The contents of three urns are as follows:
Urn 1 : 7 white, 3 black balls, Urn 2 : 4 white, 6 black balls, and Urn 3 : 2 white, 8 black balls. One of these urns is chosen at random with probabilities 0.20, 0.60 and 0.20 respectively. From the chosen urn two balls are drawn at random without replacement. If both these balls are white, what is the probability that these came from urn 3?
In a class, 5% of the boys and 10% of the girls have an IQ of more than 150. In this class, 60% of the students are boys. If a student is selected at random and found to have an IQof more than 150, find the probability that the student is a boy.
In a group of 400 people, 160 are smokers and non-vegetarian, 100 are smokers and vegetarian and the remaining are non-smokers and vegetarian. The probabilities of getting a special chest disease are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the disease. What is the probability that the selected person is a smoker and non-vegetarian?
A bag contains 1 white and 6 red balls, and a second bag contains 4 white and 3 red balls. One of the bags is picked up at random and a ball is randomly drawn from it, and is found to be white in colour. Find the probability that the drawn ball was from the first bag.
Coloured balls are distributed in four boxes as shown in the following table:
| Box | Colour | |||
| Black | White | Red | Blue | |
| I II III IV |
3 2 1 4 |
4 2 2 3 |
5 2 3 1 |
6 2 1 5 |
A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III.
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?
In answering a question on a multiple choice test a student either knows the answer or guesses. Let \[\frac{3}{4}\] be the probability that he knows the answer and \[\frac{1}{4}\] be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability \[\frac{1}{4}\]. What is the probability that a student knows the answer given that he answered it correctly?
A laboratory blood test is 99% effective in detecting a certain disease when its infection is present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1% of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
A box contains 2 blue and 3 pink balls and another box contains 4 blue and 5 pink balls. One ball is drawn at random from one of the two boxes and it is found to be pink. Find the probability that it was drawn from second box
Jar I contains 5 white and 7 black balls. Jar II contains 3 white and 12 black balls. A fair coin is flipped; if it is Head, a ball is drawn from Jar I, and if it is Tail, a ball is drawn from Jar II. Suppose that this experiment is done and a white ball was drawn. What is the probability that this ball was in fact taken from Jar II?
A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability 0.10 of giving a (false) positive result when applied to a non-sufferer. It is estimated that 0.5% of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population). Calculate the probability that: given a positive result, the person is a sufferer
A doctor is called to see a sick child. The doctor has prior information that 80% of the sick children in that area have the flu, while the other 20% are sick with measles. Assume that there is no other disease in that area. A well-known symptom of measles is rash. From the past records, it is known that, chances of having rashes given that sick child is suffering from measles is 0.95. However occasionally children with flu also develop rash, whose chance are 0.08. Upon examining the child, the doctor finds a rash. What is the probability that child is suffering from measles?
2% of the population have a certain blood disease of a serious form: 10% have it in a mild form; and 88% don't have it at all. A new blood test is developed; the probability of testing positive is `9/10` if the subject has the serious form, `6/10` if the subject has the mild form, and `1/10` if the subject doesn't have the disease. A subject is tested positive. What is the probability that the subject has serious form of the disease?
A box contains three coins: two fair coins and one fake two-headed coin is picked randomly from the box and tossed. What is the probability that it lands head up?
Solve the following:
The ratio of Boys to Girls in a college is 3:2 and 3 girls out of 500 and 2 boys out of 50 of that college are good singers. A good singer is chosen what is the probability that the chosen singer is a girl?
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?
Suppose you have two coins which appear identical in your pocket. You know that one is fair and one is 2-headed. If you take one out, toss it and get a head, what is the probability that it was a fair coin?
Refer to Question 41 above. If a white ball is selected, what is the probability that it came from Bag 3
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
There are two boxes, namely box-I and box-II. Box-I contains 3 red and 6 black balls. Box-II contains 5 red and 5 black balls. One of the two boxes, is selected at random and a ball is drawn at random. The ball drawn is found to be red. Find the probability that this red ball comes out from box-II.
Read the following passage and answer the questions given below.
|
A shopkeeper sells three types of flower seeds A1, A2, A3. They are sold is the form of a mixture, where the proportions of these seeds are 4:4:2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively.
|
Based on the above information:
- Calculate the probability that a randomly chosen seed will germinate.
- Calculate the probability that the seed is of type A2, given that a randomly chosen seed germinates.
The Probability that A speaks truth is `3/4` and that of B is `4/5`. The probability that they contradict each other in stating the same fact is p, then the value of 40p is ______.
The probability that A speaks truth is `4/5`, while the probability for B is `3/4`. The probability that they contradict each other when asked to speak on a fact is ______.
In an entrance test, there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is ______.
A jewellery seller has precious gems in white and red colour which he has put in three boxes.
The distribution of these gems is shown in the table given below:
| Box | Number of Gems | |
| White | Red | |
| I | 1 | 2 |
| I | 2 | 3 |
| III | 3 | 1 |
He wants to gift two gems to his mother. So, he asks her to select one box at random and pick out any two gems one after the other without replacement from the selected box. The mother selects one white and one red gem.
Calculate the probability that the gems drawn are from Box II.
