Probability practice · Easy

The probability that the same number appear on throwing three dice simultaneously, is

Two dice are thrown. If it is known that the sum of the numbers on the dice is less than 6 , the probability of getting a sum 3 is

If three six-faced fair dice are thrown together, the probability that the sum of the numbers appearing on the dice is 16 is

$A$ and $B$ are two independent events such that $P\left( A \right)\frac{1}{2}$ and $P\left( B \right) = \frac{1}{3},\;$ then $P$ (neither $A$ nor $B$) is equal to

5 persons $A, B, C, D$ and $E$ are in a queue of a shop. The probability that $A$ and $E$ always occur together, is

A coin is tossed 10 times. The probability of getting exactly six heads is

Two dice are tossed once. The probability of getting even number at the first die or a total of 8 is

An investment consultant predicts that the odds ageinst the price of a certain stock will go up during the next week are $2: 1$ and the odds in favour of the price remaining the same are $1: 3$. The probability that the price of the stock will go down during the next week, is

In a class of 125 students 70 passed in Mathematics, 55 in Statistic and 30 in both. The probability that a student selected at random from the class, has passed in only one subject is

There are five students $S_1, S_2, S_3, S_4$ and $S_5$ in a music class and for them there are five seats $R_1, R_2, R_3, R_4$ and $R_5$ arranged in a row, where initially the seat $R_i$ is allotted to the student $S_i, i=1,2,3,4,5$.But, on the examination day, the five students are randomly allotted the five seats. The probability that, on the examination day, the student $S_1$ gets the previously allotted seat $R_1$, and none of the remaining students gets the seat previously allotted to him/her, is

It has been found that if $A$ and $B$ play a game 12 times, $A$ wins 6 times, $B$ wins 4 times and they draw twice. $A$ and $B$ take part in a series of 3 games. The probability that they will win alternately is

Two cards are drawn successively with replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is

The odds against a certain event are 5 :2 and the odds in favour of another independent event are 6 : 5. The probability that at least one of the events will happen, is

A bag contains 10 mangoes out of which 4 are rotten, two mangoes are taken out together. If one of them is found to be good, the probability that other is also good is

For a binomial variate $X$ with $n = 6$, if $P\left( {X = 2} \right) = 9P\left( {X = 4} \right)$, then its variance is

If $X$ has a binomial distribution, $B(n,p)$with parameters $n$ and $p$ such that $P\left( {X = 2} \right) = P\left( {X = 3} \right),$ then $E\left( X \right),$ the mean of variable $X,$ is

If $E$ and $F$ are two events associated with a random experiment for which $P(E)=0.6, P(E \cup F)$ $=0.85$ and $P(E \cap F)=0.42$, then $P(F)$ is

To open a lock, a key is taken out from a collection of $n$ keys at random. If the lock is not opened with this key, it is put back into the collection and another key is tried. The process is repeated again and again. If it is given that with only one key in the collection, the lock can be opened, then the probability that the lock will open in $n$ trials, is

The probability that in the toss of two dice, we obtain the sum 7 or 11, is

The probability that randomly selected calculator from a store is of brand $r$ is proportional to $r$, $r=1,2, \ldots, 6$. Further, the probability of a calculator of brand $r$ being defective is $\frac{7-r}{21}, r=1,2, \ldots, 6$. Then the probability that a calculator randomly selected from the store being defective is

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

A random variable $X$ has the following probability distribution
$\begin{array}{l} X\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,2\,\,\,\,\,\,\,\,3\,\,\,\,\,\,\,\,4\\ P(X)\,\,\,k\,\,\,\,\,\,2k\,\,\,\,\,3k\,\,\,\,\,4k \end{array}$
Then, the mean of $X$ is

From a box containing 20 tickets marked with numbers 1 to 20, four tickets are drawn one by one. After each draw, the ticket is replaced. The probability that the largest value of tickets drawn is 15 is

If $P(A \cap B)=\frac{7}{10}$ and $P(B)=\frac{17}{20}$, then $P(A / B)$ equals to

In a maths paper there are 3 sections A, B and C. Section A is compulsory. Out of sections $B$ and $C$ a student has to attempt any one. Passing in the paper means passing in $\mathrm{A}$ and passing in $\mathrm{B}$ or $\mathrm{C}$. The probability of the student passing in $\mathrm{A}, \mathrm{B}$ and $C$ are $p, q$ and $1 / 2$ respectively. If the probability that the student is successful is $1 / 2$ then

Probability that in the toss of two dice we obtain an even sum or a sum less than 5, is

Assuming that for a husband-wife couple the chances of their child being a boy or a girl are the same, the probability of their two children being a boy and a girl is

For $k = 1,2,3$ the box ${B_k}$ contains $k$ red balls and $\left( {k + 1} \right)$ white balls,
Let $P\left( {{B_1}} \right) = \frac{1}{2},\,P\left( {{B_2}} \right) = \frac{1}{3}$ and $P\left( {{B_3}} \right) = \frac{1}{6}$
A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box ${B_2}$, is

A natural number $x$ is chosen at random from the first 100 natural numbers. The probability that $x + \frac{{100}}{x} > 50$

If $X$ is a poisson variate such that $P\left( {X = 1} \right) = P\left( {X = 2} \right)$, then $P\left( {X = 4} \right)$ is equal to