Probability practice · Easy

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is:

A number is chosen form each of two sets $A=\{1,2,3,4,5,6,7,8\}$ and $B=\{8,7,6,5,4,3,2,1\}$.
If $p_1$ is the probability that the sum of the numbers is 9 and $p_2$ is the probability that sum of the numbers is 7 , then $p_1+p_2$ is equal to

For three events $A, B$ and $C, P$ (exactly one of the events $A$ or $B$ occurs $)=P$ (exactly one of the events $B$ or $C$ occurs) $=P($ exactly one of the events $C$ or $A$ occurs $)=p$ and $P$ (all the three coents occur simultaneously) $= {p^2}$, where $0 < p < 1/2$. Then the probability of atleast one of the three events $A, B$ and $C$ occurring is

What is the probability that for S's come consecutively in the woord 'MISSISSIPPI'?

At a telephone enquiry system the number of phone calls regarding relevant enquiry follow poisson distribution with an average of 5 phone calls during 10 min time intervals. The probability that there is at the most one phone cell during a 10 min time period, is

Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(X = 4), then the sum of the mean and the variance of X is:

A bag $X$ contains 2 white and 3 black bails and another bag $Y$ contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability for the ball chosen be white, is

Two fair dice are rolled once. Then the mean of sum of the numbers on them is

Probability that a student will succeed in I.I.T. entrance test is 0.2 and that he will succeed in Roorkee entrance test is 0.5. If the probability that he will successful at both the places is 0.3, then the probability that he does not succeed at both the places is

A die is rolled, let ${E}$ be the event "die shows 4" and ${F}$ be the event "die shows even number". Then

I. ${E}$ and ${F}$ are mutually exclusive.

II. ${E}$ and ${F}$ are not mutually exclusive.

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is

The probability that certain electronic conponent fails when first used in 0.10 . If it does not fail immediately, the probability that it lasts for one year is 0.99 . The probability that a new component will last for one year is

The probability that a man can hit a target is $3/4.$ He tries 5 times. The probability that he will hit the target at least three times is

A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is

A die is tossed thrice. If event of getting an even number is a success, then the probability of getting at least two successes is

A consignment of 15 record players contains 4 defectives. The record players are selected at random, one by one, and examined. The ones examined are not put back. The probability that 9th one examined is the last defective, is

A room has 3 lamps. From a collection of 10 light bulbs of which 6 are not good, a person selects 3 at random and puts them in a socket, the Probability that he will have light, is

If three natural numbers from 1 to 100 are selected randomly, then probability that all are divisible by both 2 and 3, is

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then, the probability of 2 successes is

If $A$ and $B$ are independent events of a random experiments such that $P\left( {A \cap B} \right) = \frac{1}{6}$ and $P\left( {\bar A \cap \bar B} \right) = \frac{1}{3},\;$ then $P\left( A \right)$ is equal to

If $E$ and $F$ are two independent events such that $0 < P\left( E \right) < 1$ and $0 < P\left( F \right) < 1,\;$ then

If $P(A)=\frac{1}{4}, P(\bar{B})=\frac{1}{2}$ and $P(A \cup B)=\frac{5}{9}$ then $P(A / B)$ is

If $P\left( A \right) = 1/3,P\left( B \right) = 1/2$ and $P\left( {A \cup B} \right) = 5/6,$ then events $A$ and $B$ are

A bag contains 6 white and 6 black socks. A man randomly takes out two socks from the bag. The probability that socks are the same colour is:

Six dice are thrown simultaneously. The probability that all of them show the same face, is

A number $x$ is chosen at random from the set $\{1,2,3, \ldots, 100\}$. Let $p=$ probability that $x$ is divisible by 19 and $q=$ probability that $x$ is divisible by 31, then $p+q$ is equal to

Three-digit numbers are formed using the digits $0 ,$ $1,2,3,4,5$ without repetition of digits. If a number is chosen at random, then the probability that the digits either increase or decrease, is

If $n\left( A \right) = 8$ and $n\left( {A \cap B} \right) = 2,$ then $n\left[ {{{\left( {A \cap B} \right)}^\prime } \cap A} \right]$ is equal to

Each of the persons $A$ and $B$ independently tosses three fair coins. The probability that both of them get the same number of heads is

For the three events $A,\,B$ and $C$, $P$ (exactly one of the events $A$ or $B$ occurs) $= \,P$ (exactly one of the events $B$ or $C$ occurs) $- P$ (exactly one of the events $C$ or $A$ occurs) $= \,p$ and $P$ ( all the three events occur simultaneously) $= {p^2},\;$ where $0 < p < \frac{1}{2}$. Then, the probability of at least one of the three events $A$, $B$ and $C$ occuring, is