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Syllabus

a letter is known to have come from either TATA NAGAR or CALCUTTA on the envelope just two consecutive letters TA are visible, what is the probability that the letter has come from 1. CALCUTTA 2. TATA NAGAR........

bag 1 contains 3 red and 4 black balls and bag 2 contains 4 red and 5 black balls. two balls are transferred at random from bag 1 to bag 2 and then a ball is drawn from bag 2. the ball so drawn is found to be red in colour. find the probability that the transferred balls were both black.

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.

^{6}C2 how will we solve thisAssuming that the chance of a traffic accident in a day in a street of Delhi is 0.001.

On how many days, out of a total of 500 days can we expect (I) no accident (ii) more than 3 accidents, if there are 1000

such streets in the whole city. ( use 1/e = 0.3679)??

If A and B are two independent events such that P(not A intersection B) = 2/15 and P(A intersection not B) =1/6, then find P(B)

what is meant by unbiased die and biased die ?

Three balls are drawn one by one without replacement from a bag containing 5 white and 4 green balls. FInd the probability distribution of no. of green balls drawn?

is psa exam going to hv ne effect on 12 board exam??? will it effect jee in any way......experts plz do give me some useful answers on these issues....

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denotes the larger of the two numbers obtained. Find E(X).

The probability that a student entering a university will graduate is 0.4. Find out the probability that out of 3 students of the university:

1. non will graduate

2. only one will graduate

3. All will graduate

How many times must a man toss a fair coin so that the probability of having at least one head is more than 80%?

where as the rest of the coins are fair. A coin is picked up at random from the bag and is

tossed. If the probability that the toss results in a head is 31/42

, determine the value of n.

A can hit a target 4 times in 5 shots b 3 times in 4 shots and c 2 times in 3 shots. they fire a volley. what is the probability that 2 shots at least hit (4 marks)

In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices and only one correct option. The probability that he guess is 1

are drawn at random. Probability that they are of the different colours is

A biased die is twice as likely to show an even number as an odd number. The die is rolled three times. If occurrence of an even number is considered a success, then write the probability ditribution of number of successes. Also find the mean number of success.

A man is known to speak truth 3 out of 4 times.He throws a die & reports that it is a six.Find the probability that it is actually a six.

A box contains 12 items of which 3 are defective.A sample of 3 items is selected from the box.Let X denotes the number of defective items in a sample.Find the probability distribution of X.

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.

pls xplain the steps

A man takes a step forward with probability of 0.4 and backwards with probability of 0.6.Find probability that at the end of eleven steps, he is just one step away from the starting point..

a bag contains 30 tickets numbered from 1 to 30. five tickets are drawn at random and arrenged in increasing order find the probability that the third number is 20.

A & B take turns in throwing two dice.The first to throw a sum 1o,being awarded.Show that if A has the first throw, their chances of winning is at the ratio of 12:11.

A bag contains 4 balls. Two balls are drawn at random and are found to be white. What is the probability that all balls are white?

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.?

pls xplain me the solution

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

(1) LONDON

(2) CLIFTON

In shuffling a pack of cards,

four are accidently dropped, find the chance that the dropped cards should be one from each suit.twelve balls are distributed among three boxes ,find the probability that the first box will contain 3 balls .... and also explain how we solve these type of prblms ....and sum stategy to make strong probability

A bag contains 4 balls.Two balls are drawn at random, and are found to be white. What is the probability that all balls are white ?

2 integers are selected at random from 1 to 11 . if the sum is even .find the probability that both numbers are odd

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of the number of successes and hence find its mean

A and B throw a dice alternatively till one of them gets a ‘6’and wins the game. Find their respective probabilities of winning,if A starts first??

ins)= P(S)+ P(FFS)+ P(FFFFS)=given belowP(A wand so on.

step 2 =1/6/1-25/36 = 6/11 please tell me fast.how step 2 came

4 studentsis selected at random from a group consisting of8 boysand4 girls. Given that there isat least one girlin the committee. Calculate the probability that there are exactly 2 girls in the committee.?three groups of children contain 3 girls and 1 boy : 2 girls and 4 boys :and 1 girls and 3 boys respectively. one children is selected at random from each group. find the chance that the three selected comprise 1 girl and 2 boys.

An urn contains 10 white and 3 black balls. another urn contains 3 white and 5 black balls. Two are drawn from the first urn and put into the second urn and then a ball is drawn from the latter. Find the probability that it is a white ball.

How many different ways can be used to register on an internet website, using x, y and z, and digits 1, 2, 3, 4 and 5?

Consider an experiment of tossing a coin.If the coin shows heads,toss it again but if it shows tails,then throw a die.Find the conditional probability of event that 'the die shows a number greater than 4' given that 'there is atleast one tail'.

Q.1 A speaks truth in 60% of the case and B in 90% of the cases. In what percentage of case are they likely to contradict each other in stating the same fact?

Q.2 A problem in mathematics is given to three studenys (A, B, C)whose chances of solving it are 1/3, 1/5 and 1/6 respectively. Find the probability that(i) one of them is able to solve the problem correctly. (ii) any two out of A, B, C will solve the problem?

A and B throw a die alternatively till one of them gets a '6' and wins the game. find their respective probablilites of winning, if A syarts first.

A pair of dice is thrown 200 times. If getting a sum of 9 is considered a success, find the mean and varience of the number of successes.

The content of Urn 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 II : 4 white, 5 black and 3 red balls

one urn is choosen and two balls are drawn. They happen to be white and red. What is the probability that they come from urn III ?

There are two bags.Bag1 contains 5 white and 3 black balls and bag 2 contains 3 white and 5 black balls.Two balls are drawn from bag1 and put into bag2 and then two balls are drawn from bag2. Find the probability that the bals drawn from bag2 are white and black?A man takes astep forward with probability 0.4 and backward with probability 0.6 find the the probability that at the end of eleven steps he is one step away from the starting point

noted and the pack is again reshuffled without replacing the card.

Another card is then drawn. What is the probability that the first card is a

spade and the second is a Black King.

The PROBABILITY of a shooter hitting a target is 3/4. How many minimum no. of times must he/she fire so that the probability of hitting the target atleast once is more than 0.99?????

a lady gives a dinner party to six guests. the number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is ?

Suppose 5 men out of 100 and 25 women out of 1000 are good orator. An orator is chosen at random. Find the probability that a male person is selected. Assume that there are equal number of men and women.

Two bags A and B contain 4 white balls and 3 black balls ,and 2 white balls and 2 black balls respectively .From bag A two balls are transferred to bag B.find the probability of drawing

1.2 white ball from bag B

2. 2 black balls from bag B

3.1 white ball and 1 black ball from bag B

^{In 3 trials of a binomial distribution, the probability }of exactly 2 successes is 9 times the probability of 3 successes. Find the probability of success in each trial.find the probability distribution of the number of doublets in 4 throws of a pair of dice.

In a random arranngement of the letters of the word " COMMERCE " , find the probability that all vowels come together ..

Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

Two cards are drawn without replacement from a well-shuffled deck of 52 cards. Determine the probablity distribution of the number of face cards.

Three numbers are chosen at random without replacement from {1 , 2, 3,...8} .The propability that thier minimum is 3 , given that their maximum is 6. is ..ans. is 1/5.

plzz explain..

An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.

A bag contains tickets numbered 1 to 30. Three tickets are drawn at random from the bag. What is the probability that the maximum number of the selected tickets exceeds 25.

A random variable X has the following probability distribution.

X

0

1

2

3

4

5

6

7

P (X)

0

k2

k2

k3

kk^{2}2

k^{2}7

k^{2}+kDetermine

(i)k(ii)P (X < 3)(iii)P (X > 6)(iv)P (0 < X < 3)A bag contains 3 red balls and 4 white balls. Two balls are drawn one after the other without replacement at random from the bag. If the second ball drawn is given to be white, what is the probability that the first ball drawn is also white?

Pls help as early as possible...

The probability that the contractor will get a plumbing contract is 2/3 and an electric contract is 4/9 .If the probability of getting at least one contract is 4/5 .Find the probability that he will get both the projects