Probability PYQs - Last 5 Years

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.