Recent questions in Probability

There are 5 cards numbered 1 to 5,one number on one card.Two cards are drawn at random without replacement.Let X denote the sum of the numbers on two cards drawn.Find the mean and variance of X.

asked Jan 10, 2013 by sreemathi.v

1 answer

A die is tossed twice.A 'success' is getting an even number on a toss.Find the variance of the number of successes.

asked Jan 9, 2013 by sreemathi.v

1 answer

Two cards are drawn successively without replacement from a well shuffled deck of cards.Find the mean and standard variation of the random variable X where X is the number of aces.

asked Jan 9, 2013 by sreemathi.v

1 answer

A bag contains (2n+1) coins.It is known that n of these coins have a head on both sides 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 $\Large \frac{31}{42}$,determine the value of n.

asked Jan 9, 2013 by sreemathi.v

1 answer

The probability distribution of a random variable x is given as under:\[P(X=x)=\left \{\begin{array}{1 1}kx^2 & for\;x=1,2,3\\2kx & for\;x=4,5,6\\0 & otherwise\end{array}\right.\]Where k is a constant.Calculate\[(i)\;E(X)\quad(ii)\;E(3X^2)\quad(iii)\;P(X\geq 4)\]

asked Jan 9, 2013 by sreemathi.v

1 answer

The probability distribution of a discrete random variable X is given as under:

asked Jan 9, 2013 by sreemathi.v

1 answer

Let X be a discrete random variable whose probability distribution is defined as follows:\[P(X=x)=\left \{\begin{array}{1 1}k(x+1) & for\;x=1,2,3,4\\2kx & for\;x=5,6,7\\0 & otherwise\end{array} \right.\]where k is a constant. Calculate\[(i)\;the\;value\;of\;k\quad(ii)\;E(X)\quad(iii)\;standard\;deviation\;of\;X\]

asked Jan 9, 2013 by sreemathi.v

1 answer

An item is manufactured by three machines A,B and C.Out of the total number of items manufactured during a specified period,50% are manufactured on A,30% on B and 20% on C.2% of the items produced on A and 2% of items produced on B are defective,and 3% of these produced on C are defective.All the items are stored at one godown.One item is drawn at random and is found to be defective.What is the probability that it was manufactured on machine A?

asked Jan 9, 2013 by sreemathi.v

1 answer

By examining the chest X ray,the probability that TB is detected when a person is actually suffering is 0.99.The probability of an healthy person diagnosed to have TB Is 0.001.In a certain city,1 in 1000 people suffers from TB.A person is selected at random and is diagnosed to have TB.What is the probability that he actually has TB?

asked Jan 9, 2013 by sreemathi.v

1 answer

There are three urns containing 2 white and 3 black balls,3 white and 2 black balls,and 4 white and 1 black balls,respectively.There is an equal probability of each urn being chosen.A ball is drawn at random from the chosen urn and it is found to be white.find the probability that the ball drawn was from the second urn.

asked Jan 9, 2013 by sreemathi.v

1 answer

There are two bags,one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls.A die is thrown.If it shows up 1 or 3,a ball is taken from the 1st bag,but it shows up any other number,a ball is chosen from the second bag.Find the probability of choosing a black ball.

asked Jan 9, 2013 by sreemathi.v

1 answer

A letter is known to have come either from TATA NAGAR or from CALCUTTA.On the envelope,just two consecutive letter TA are visible.What is the probability that the letter came from TATA NAGAR.

asked Jan 9, 2013 by sreemathi.v

2 answers

A shop keeper sells three types of flower seeds $A_1,A_2 and\;A_3$.They are sold as a mixture where the proportions arev4:4:2 respectively.The germination rates of the three types of seeds are 45%,60% and 35%.Calculate the probability\[\begin{array}{1 1}(i)\;of\;a\;randomly\;chosen\;seed\;to\;germinate\\(ii)\;that\;it\;will\;not\;germinate\;given\;that\;seed\;is\;of\;type\;A_3\\(iii)\;that\;it\;is\;of\;the\;type\;A_2\;given\;that\;a\;randomly\;chosen\;seed\;does\;not\;germinate\end{array}\]

asked Jan 9, 2013 by sreemathi.v

1 answer

Three bags contain a number of red and white balls as follows:

asked Jan 9, 2013 by sreemathi.v

1 answer

Three bags contain a number of red and white balls as follows:

asked Jan 9, 2013 by sreemathi.v

1 answer

An urn contains m white and n black balls,A ball is drawn at random and is put back into the urn along with k additional balls of the same color as that of the ball drawn,A ball is again drawn at random.Show that the probability of drawing a white ball now does not depend on k.

asked Jan 9, 2013 by sreemathi.v

1 answer

Two dice are tossed.Find whether the following two events A and B are independent.\[A=(x,y):x+y=11\quad B=(x,y):x=5\]where (x,y) denotes a typical sample point.

asked Jan 9, 2013 by sreemathi.v

1 answer

A and B throw pair of dice alternately.A wins the game if he gets a total of 6 and B wins if she gets a total of 7.It A starts the game,find the probability of winning the game by A in third throw of the pair of dice.

asked Jan 9, 2013 by sreemathi.v

1 answer

Find the variance of the distribution.

asked Jan 9, 2013 by sreemathi.v

1 answer

The random variable X can take only the values 0,1,2.Given that P(x=0)=P(X=1)=P and that E($X^2$)=E[X],find the value of p.

asked Jan 9, 2013 by sreemathi.v

1 answer

Find the probability distribution of the maximum of two scores obtained when a die is thrown twice .Determine also the mean of the distribution.

asked Jan 9, 2013 by sreemathi.v

1 answer

Two natural numbers r,s are drawn one at a time,without replacement from the set S=1,2,3,......,n.Find $P[r\leq p|s\leq p],where \;p\in S$

asked Jan 9, 2013 by sreemathi.v

1 answer

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?

asked Jan 9, 2013 by sreemathi.v

1 answer

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?

asked Jan 9, 2013 by sreemathi.v

1 answer

A factory produces bulbs,The probability that any one bulb is defective is $\Large \frac{1}{50}$ and they are packed in boxes of 10.From a single box,find the probability that\begin{array}{1 1}(i)\;none\;of\;the\;bulbs\;is \;defective.\\(ii)\;exactly\;two\;bulbs\;are\;defective\\(iii)\;more\;than\;8\;bulbs\;work\;properly\end{array}

asked Jan 9, 2013 by sreemathi.v

1 answer

Two probability distributions of the discrete random variable X and Y are given below.

asked Jan 9, 2013 by sreemathi.v

1 answer

Two biased dice are thrown together.For the first die $P(6)=\Large \frac{1}{2}$,the other scores being equally likely while for the second die,$P(1)=\Large \frac{2}{5}$ and the other scores are equally likely.Find the probability distribution of 'the number of ones seen'.

asked Jan 9, 2013 by sreemathi.v

1 answer

A die is thrown three times.Let X be 'the number of twos seen'.Find the expectation of X.

asked Jan 9, 2013 by sreemathi.v

1 answer

A biased die is such that $P(4)=\Large \frac{1}{10}$ and other scores being equally likely.The die is tossed twice.If X is the number of fours seen',find the variance of the random variable X.

asked Jan 9, 2013 by sreemathi.v

1 answer

For the following probability distribution determine standard deviation of the random variable X.

asked Jan 9, 2013 by sreemathi.v

1 answer

The probability distribution of a random variable X is given below:

asked Jan 9, 2013 by sreemathi.v

0 answers

Consider the probability distribution of a random variable X.

asked Jan 9, 2013 by sreemathi.v

1 answer

A lot of 100 watches is known to have 10 defective watches.If 8 watches are selected(one by one with replacement) at random,what is the probability that there will be at least one defective watch?

asked Jan 9, 2013 by sreemathi.v

1 answer

The probability of a man hitting a target is 0.25.He shoots 7 times.What is the probability of his hitting at least twice?

asked Jan 9, 2013 by sreemathi.v

1 answer

Ten coins are tossed.What is the probability of getting at least 8 heads?

asked Jan 9, 2013 by sreemathi.v

1 answer

A die is thrown 5 times.Find the probability that an odd number will come up exactly three times.

asked Jan 9, 2013 by sreemathi.v

1 answer

Four cards are successively drawn with out replacement from a deck of 52 playing cards.What is the probability that all the four cards are kings?

asked Jan 9, 2013 by sreemathi.v

1 answer

A box has 5 blue and red balls.One ball is drawn at random and not replaced.Its colour is also not noted .The another ball is drawn at random.what is the probability of second ball being blue?

asked Jan 9, 2013 by sreemathi.v

1 answer

Bag I contains 3 black and 2 white balls,Bag II contains 2 black and 4 white balls.A bag and a ball is selected at random .Determine the probability of selecting a black ball.

asked Jan 9, 2013 by sreemathi.v

1 answer

A bag contains 4 white and 5 black balls.Another bag contains 9 white and 7 black balls.A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag.Find the probability that the ball drawn is white.

asked Jan 9, 2013 by sreemathi.v

1 answer

Suppose 10,000 tickets are sold in a lottery each for Re1.First prize is of Rs 3000 and the second prize is of Rs 2000.There are three third prizes of Rs 500 each.If you buy one ticket,what is your expectation.

asked Jan 8, 2013 by sreemathi.v

1 answer

Three dice are thrown at the same time.Find the probability of getting three two's,if it is known that the sum of the numbers on the dice was six.

asked Jan 8, 2013 by sreemathi.v

1 answer

In a dice game, a player pays a stake of Re1 for each throw of a die.She receives Rs 5 if the die shows a 3,Rs 2 if the die shows a 1 or 6,and nothing otherwise.What is the player's expected profit per throw over a long series of throws?

asked Jan 8, 2013 by sreemathi.v

1 answer

If X is the number of tails in three tosses of a coin ,determine the standard deviation of X.

asked Jan 8, 2013 by sreemathi.v

1 answer

Prove that\begin{array}{1 1}(i)\;P(A)+P(A\cap B)+P(A\cap \bar{B})\\(ii)\;P(A\cup B)=P(A\cap B)+P(A\cap\bar{B})+P(\bar{A}\cap\bar{B})\end{array}

asked Jan 8, 2013 by sreemathi.v

1 answer

A discrete random variable X has the probability distribution given as below:

asked Jan 8, 2013 by sreemathi.v

1 answer

Let $E_1$ and $E_2$ be the two independent events.Such that $P(E_1)=p_1$ and $P(E_2)=p_2$.

asked Jan 8, 2013 by sreemathi.v

1 answer

Three events A,B and C have probabilities $\Large \frac{2}{5},\frac{1}{3}$ and $\Large \frac{1}{2}$,respectively.Given that $P(A\cap C)=\frac{1}{5}\;and\;P(B\cap C)=\frac{1}{4}$,find the value of $P(C|B)\; and \;P(A'\cap C').$

asked Jan 8, 2013 by sreemathi.v

1 answer

A and B are two events such that $P(A)=\frac{1}{2},P(B)=\frac{1}{3} and\; P(A\cap B)=\frac{1}{4}$.Find:\[(i)\;P(A|B)\quad(ii)\;P(B|A)\quad(iii)\;P(A'|B)\quad(iv)\;P(A'|B')\]

asked Jan 8, 2013 by sreemathi.v

1 answer

Explain why the experiment of tossing a coin three times is said to have binomial distribution.

asked Jan 8, 2013 by sreemathi.v

1 answer

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