Probability

Let E and F be two independent events. The probability that both E and F happen is \({1 \over {12}}\) and the probability that neither E nor F happens is \({1 \over {2}}\), then a value of \({{P\left( E \right)} \over {P\left( F \right)}}\)...

Three persons P, Q and R independently try to hit a target. I the probabilities of their hitting the target are \({3 \over 4},{1 \over 2}\) and \({5 \over 8}\) respectively, then the probability that the target is hit by P or Q but not by R...

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with
replacement, then the variance of the number of green balls drawn is :

If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as
well as absolute difference are both multiple of 4, is :

For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P
(Exactly one of C or A occurs) = \({1 \over 4}\)
and P(All the three events occur simultaneously) = \({1 \over {16}}\).
Then the
probabilit...

If A and B are any two events such that P(A) = \({2 \over 5}\) and P (A \(\cap\) B) = \({3 \over {20}}\), hen the conditional probability, P(A \(\left| {} \right.\)(A' \(\cup\) B')), where A' denotes the complement of A, is equal to :

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is :

Let two fair six-faced dice \(A\) and \(B\) be thrown simultaneously. If \({E_1}\) is the event that die \(A\) shows up four, \({E_2}\) is the event that die \(B\) shows up two and \({E_3}\) is the event that the sum of numbers on both dice...

If \(12\) different balls are to be placed in \(3\) identical boxes, then the probability that one of the boxes contains exactly \(3\) balls is :

Let \(A\) and \(B\) be two events such that \(P\left( {\overline {A \cup B} } \right) = {1 \over 6},\,P\left( { {A \cap B} } \right) = {1 \over 4}\) and \(P\left( {\overline A } \right) = {1 \over 4},\) where \(\overline A\) stands for the...

A multiple choice examination has \(5\) questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get \(4\) or more correct answers just by guessing is :

Three numbers are chosen at random without replacement from \(\left\{ {1,2,3,..8} \right\}.\) The probability that their minimum is \(3,\) given that their maximum is \(6,\) is :

Consider \(5\) independent Bernoulli's trials each with probability of success \(p.\) If the probability of at least one failure is greater than or equal to \({{31} \over 32},\) then \(p\) lies in the interval :

If \(C\) and \(D\) are two events such that \(C \subset D\) and \(P\left( D \right) \ne 0,\) then the correct statement among the following is :

Four numbers are chosen at random (without replacement) from the set \(\left\{ {1,2,3,....20} \right\}.\)
Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is \({1 \over {85}}.\)
Statement -...

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is :

In a binomial distribution \(B\left( {n,p = {1 \over 4}} \right),\) if the probability of at least one success is greater than or equal to \({9 \over {10}},\) then \(n\) is greater than :

One ticket is selected at random from \(50\) tickets numbered \(00, 01, 02, ...., 49.\) Then the probability that the sum of the digits on the selected ticket is \(8\), given that the product of these digits is zer, equals :

It is given that the events \(A\) and \(B\) are such that
\(P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1 \over 2}\) and \(P\left( {B|A} \right) = {2 \over 3}.\) Then \(P(B)\) is :

A die is thrown. Let \(A\) be the event that the number obtained is greater than \(3.\) Let \(B\) be the event that the number obtained is less than \(5.\) Then \(P\left( {A \cup B} \right)\) is :

Two aeroplanes \({\rm I}\) and \({\rm I}\)\({\rm I}\) bomb a target in succession. The probabilities of \({\rm I}\) and \({\rm I}\)\({\rm I}\) scoring a hit correctly are \(0.3\) and \(0.2,\) respectively. The second plane will bomb only if...

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly \(9\) twice is :

At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of \(5\) phone calls during \(10\) minute time intervals. The probability that there is at the most one phone cal...

A random variable \(X\) has Poisson distribution with mean \(2\).
Then \(P\left( {X > 1.5} \right)\) equals :

Let \(A\) and \(B\) two events such that \(P\left( {\overline {A \cup B} } \right) = {1 \over 6},\) \(P\left( {A \cap B} \right) = {1 \over 4}\) and \(P\left( {\overline A } \right) = {1 \over 4},\) where \({\overline A }\) stands for comp...

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

The mean and the variance of a binomial distribution are \(4\) and \(2\) respectively. Then the probability of \(2\) successes is :

The probability that \(A\) speaks truth is \({4 \over 5},\) while the probability for \(B\) is \({3 \over 4}.\) The probability that they contradict each other when asked to speak on a fact is :

Events \(A, B, C\) are mutually exclusive events such that \(P\left( A \right) = {{3x + 1} \over 3},\) \(P\left( B \right) = {{1 - x} \over 4}\) and \(P\left( C \right) = {{1 - 2x} \over 2}\) The set of possible values of \(x\) are in the i...

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is :

The mean and variance of a random variable \(X\) having binomial distribution are \(4\) and \(2\) respectively, then \(P(X=1)\) is :

A problem in mathematics is given to three students \(A,B,C\) and their respective probability of solving the problem is \({1 \over 2},{1 \over 3}\) and \({1 \over 4}.\) Probability that the problem is solved is :

A dice is tossed \(5\) times. Getting an odd number is considered a success. Then the variance of distribution of success is :

\(A\) and \(B\) are events such that \(P\left( {A \cup B} \right) = 3/4\),\(P\left( {A \cap B} \right) = 1/4,\)
\(P\left( {\overline A } \right) = 2/3\) then \(P\left( {\overline A \cap B} \right)\) is :