Probability

Probability of at least one of the events A and B occur is $0.6$. If A and B occur simultaneously with probability $0.2$, then $P(\bar{A}) + P(\bar{B})$ is

Probability of occurrence of an event A is $\dfrac{1}{2}$ and that of B is $\dfrac{3}{10}$. If A and B are mutually exclusive, then the probability of occurrence of neither A nor B is

Probability of obtaining an even prime number on each die when a pair of dice is rolled is

The probability that a man and his wife live after $20$ years are $\dfrac{1}{4}$ and $\dfrac{1}{3}$ respectively. The probability that neither the man nor his wife live after $20$ years is

Recent studies suggest that $12\%$ of the world population is left handed. Depending on parents' hand usage, the chances of having left handed children are as follows:A: Both parents are left handed, chances of having left handed children $...

Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is $\frac{2}{5}$. If she visits temple $A, \frac{1}{3}$ is the probability that she meets her friend, whereas it is $\frac{2}{7}$ if she ...

If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$, then which of the following is correct?

If A and B are two non-mutually exclusive events such that $\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\mathrm{P}(\mathrm{B} \mid \mathrm{A})$, then

Consider the following statements.
Statement (I): If E and F are two independent events, then $E^{\prime}$ and $F^{\prime}$ are also independent.
Statement (II): Two mutually exclusive events with non-zero probabilities of occurrence cannot...

A die has two face each with number ' 1 ', three faces each with number ' 2 ' and one face with number ' 3 '. If the die is rolled once, then $\mathrm{P}(1$ or 3$)$ is

A random experiment has five outcomes $\mathrm{w}_1, \mathrm{w}_2, \mathrm{w}_3, \mathrm{w}_4$ and $\mathrm{w}_5$. The probabilities of the occurrence of the outcomes $w_1, w_2, w_3, w_4$ and $w_5$ are respectively $\frac{1}{6}, a, b$ and $...

If a random variable $X$ follows the binomial distribution with parameters $n=5, p$ and $P(X=2)=9 P(X=3)$, then $p$ is equal to

A random variable $X$ has the following probability distribution:

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A die is thrown 10 times. The probability that an odd number will come up at least once is

If \(A\) and \(B\) are events, such that \(P(A)=\frac{1}{4}, P(A / B)=\frac{1}{2}\) and \(P(B / A)=\frac{2}{3}\), then \(P(B)\) is

Let \(A=\{x, y, z, u\}\) and \(B=\{a, b\}\). A function \(f: A \rightarrow B\) is selected randomly. The probability that the function is an onto function is

A bag contains \(2 n+1\) coins. It is known that \(n\) of these coins have head on both sides whereas, the other \(n+1\) coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $$\frac{31}...

If \(A\) and \(B\) are two independent events such that \(P(\bar{A})=0.75, P(A \cup B)=0.65\) and \(P(B)=x\), then find the value of \(x\).

A pandemic has been spreading all over the world. The probabilities are 0.7 that there will be a lockdown, 0.8 that the pandemic is controlled in one month if there is a lockdown and 0.3 that it is controlled in one month if there is no loc...

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{2}, P(B)=\frac{1}{2}\) and \(P(A \mid B)=\frac{1}{4}\), then \(P\left(A^{\prime} \cap B^{\prime}\right)\) is

Find the mean number of heads in three tosses of a fair coin.

A car manufacturing factory has two plants \(X\) and \(Y\). Plant \(X\) manufactures \(70 \%\) of cars and plant \(Y\) manufactures \(30 \%\) of cars. \(80 \%\) of cars at plant \(X\) and \(90 %\) of cars at plant \(Y\) are rated as standar...

If \(A, B\) and \(C\) are three independent events such that \(P(A)=P(B)=P(C)=P\), then \(P\) (at least two of \(A, B\) and \(C\) occur) is equal to

If \(P(A)=0.59, P(B)=0.30\) and \(P(A \cap B)=0.21\) then \(P\left(A^{\prime} \cap B^{\prime}\right)\) is equal to

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

Given that, \(A\) and \(B\) are two events such that \(P(B)=\frac{3}{5}, P\left(\frac{A}{B}\right)=\frac{1}{2}\) and \(P(A \cup B)=\frac{4}{5}\), then \(P(A)\) is equal to

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{3}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{6}\), then \(P\left(A^{\prime} / B\right)\) is

A die is thrown 10 times, the probability that an odd number will come up at least one time is

If \(A, B, C\) are three mutually exclusive and exhaustive events of an experiment such that \(P(A)=2 P(B)=3 P(C)\), then \(P(B)\) is equal to

Events \(E_1\) and \(E_2\) from a partition of the sample space \(S\). \(A\) is any event such that \(P\left(E_1\right)=P\left(\dot{E}_2\right)=\frac{1}{2}, P\left(E_2 / A\right)=\frac{1}{2}\) and \(P\left(A / E_2\right)=\frac{2}{3}\), then...

The probability of solving a problem by three persons \(A, B\) and \(C\) independently is \(\frac{1}{2}, \frac{1}{4}\) and \(\frac{1}{3}\) respectively. Then the probability of the problem is solved by any two of them is

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set \(S=\{1,2,3,4,5,6,7\}\) and reports that it is even. The probability that is actually even is

If '\(X\)' has a binomial distribution with parameters \(n=6, p\) and \(P(X=2)=12\), \(P(X=3)=5\) then \(P=\)

If \(A\) and \(B\) are two events of a sample space \(S\) such that \(P(A)=0.2, P(B)=0.6\) and \(P(A \mid B)=0.5\) then \(P\left(A^{\prime} \mid B\right)=\)

A random variable '\(X\)' has the following probability distribution

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Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is consonant is

A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, then another ticket is drawn without replacing the first one. The probability that both the tickets may show even numbers is

A flashlight has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then the probability that all 3 are dead is

In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is

The probability of happening of an event $A$ is 0.5 and that of $B$ is 0.3 . If $A$ and $B$ are mutually exclusive events, then the probability of neither $A$ nor $B$ is

If $A$ and $B$ are mutually exclusive events, given that $P(A)=\frac{3}{5}, P(B)=\frac{1}{5}$, then $P(A$ or $B)$ is

Two events $A$ and $B$ will be independent if

A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn one by one with replacement and atmost one is defective, is

The probability distribution of $X$ is
$$ \begin{array}{|c|l|c|c|c|} \hline \boldsymbol{X} & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{P}(\boldsymbol{X}) & 0.3 & k & 2 k & 2 k \\ \hline \end{array} $$
\(\text { The value of } k \text { is }\)