List of top Mathematics Questions on Probability

If the probability that a person suffers a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ will suffer a bad reaction is:

A random variable $X$ has the following probability distribution:
$X = x$: 0, 1, 2, 3, 4, 5
$P(X=x)$: $k$, $3k$, $5k$, $7k$, $9k$, $11k$
Then the value of $k$ is:

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 three apply for the same house is:

A fair die is rolled indefinitely. Player A wins if two consecutive rolls show 3 or 5, and player B wins if two consecutive rolls show 1 or 2 or 4 or 6. The probability that player A wins in the long run is

Bag A contains 3 white and 5 black balls while bag B contains 4 white and 3 black balls. A ball is selected at random from bag A and put in bag B. If a ball is now selected at random from bag B then the probability that this ball is white ball is...

The probability that a bomb will hit the target is \(0.8\). Out of 6 bombs dropped, probability that at least 1 will miss the target is...

Let \(a\) be an integer selected at random from the set \(\{0,1,2,3,\ldots ,9\}\). The probability that the equation \(ax^2-ax+1 = 0\) has real roots is ...

If the probabilities of a student succeeding in the entrance tests for institutes A, B and C are \(0.6\), \(0.5\) and \(0.4\) respectively, while the probability of succeeding in both A and B is \(0.3\), in both B and C is \(0.2\), in both A and C is \(0.2\), and in all three is \(0.1\), then the probability that the student succeeds in exactly one of these tests is......

If a discrete random variable \(X\) takes the values \(1,2,3,4\) such that \(2P(X = 1) = 3P(X = 2) = P(X = 3) = 5P(X = 4)\), then \(P(X = 4) = \ldots\)

In a test, there are 5 questions of the 'true or false' type. No student has got all the answers correct and the sequence of answers for every student is unique. The maximum number of students who could have appeared for the test is....

Three ships A, B, C sail from England to India. If the odds in favour of their safe arrival are 2:5, 3:7 and 6:11 respectively, then the probability that the exactly two ships arrive safely is

A random variable X has the following probability distribution

X	1	2	3	4	5	6	7	8
P(X=\(x\))	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

For the event E = { X is a prime number } and F = { X < 4 }, P(E\(\cup\)F) =

If 6 boys and 3 girls are to be seated in a row for a photograph, then the probability that the end seats are occupied by the girls and no two girls are side by side is

A random variable X has the following probability distribution

\(X = x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)
\(P(X = x)\)	\(0.15\)	\(0.23\)	\(0.10\)	\(0.12\)	\(0.20\)	\(0.08\)	\(0.07\)	\(0.05\)

For the events \(E = \{X\text{ is a prime number}\}\), \(F = \{X < 4\}\), \(P(E\cup F)\) is

If events A and B are such that \(P(A) = \frac{1}{4}\), \(P(A\cap B) = \frac{1}{10}\) and \(P(A/B) = 2P(B/A)\) then \(P(B) =\)...........

Two cards are drawn at random from a standard pack of \(52\) cards. Then the probability that the draw consists of exactly one face card and exactly one ace card is...

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is \(3/5\), then find the number of yellow balls.

Probability of getting at least one head in two coin tosses: ____.

If \( \alpha \) and \( \beta \) (\( \alpha<\beta \)) are the roots of the equation \( (-2 + \sqrt{3})(\sqrt{x} - 3) + (x - 6\sqrt{x}) + (9 - 2\sqrt{3}) = 0 \), \( x \ge 0 \), then \( \sqrt{\frac{\beta}{\alpha}} + \sqrt{\alpha\beta} \) is equal to:

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

Which of the following can not be the probability of an event ?

Meena calculates that the probability of her winning the first prize in a lottery is $0.08$. If total $800$ tickets were sold, the number of tickets bought by her, is

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

Which of the following can not be the probability of an event ?