MCA Entrance Previous Year Question Bank

Let $X$ and $Y$ be two independent, identically distributed Bernoulli random variables with a common probability mass function: $P(X=1)=\frac{1}{2}$ and $P(X=0)=\frac{1}{2}$. If $Z=XY$, then the distribution of $Z$ is:

Let $A_1,A_2,A_3$ be events in a sample space with the condition $A_1\cap A_2\ne \varphi$. Then, which of the following is always true?

A die is rolled twice independently. What is the probability that either the first die shows a number no less than $4$ or the second die shows at least $4$?

A random variable $X$ has the probability distribution:

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

$A$, $B$ and $C$ are shooting with probabilities $\frac{3}{5}$, $\frac{2}{5}$, $\frac{3}{4}$ respectively. The probability that the target is hit by at least two shots is:

$A$ and $B$ are independent events. The probability that both will occur is $1/8$ and that neither of them occur is $3/8$. If P(A) > P(B), find $P(B)$.

A bag contains 5 red and 3 white marbles and another bag contains 2 red and 6 white marbles. 2 marbles are drawn at random from each bag. What is the probability that the marbles drawn are of same colours:

A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is:

A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is:

A bag contains 6 red and 4 green balls. A fair dice is rolled and a number of balls equal to that appearing on the dice is chosen from the urn at random. The probability that all the balls selected are red is: