MCA Entrance Previous Year Question Bank

The probability of getting a job for a person is x/3. If the probability of not getting the job is 2/3, then the value of x is

How many distinguishable permutations of the letters are there in the word BANANA?

Normals distribution is also known as

Given three identical boxes and each containing two balls. contains two golden balls,

contains two silver balls and contains one silver and one golden ball. Conditional

probabilities that the golden ball is drawn from are ______________ respectively.

Given a set of events $E_1,E_2,\dots ,E_n$ defined on the sample space $S$ such that:

(i) $E_i\cap E_j=\varnothing$ (ii) ${\bigcup }_{i=1}^n{E}_i=S$ (iii) P(E_i) > 0,\ \forall i = 1,2,\ldots,n

Then the events are:

Consider n events $E_1,E_2,\dots ,E_n$ with respective probabilities $p_1,p_2,\dots ,p_n$.

If $P(E_1{E}_2\dots E_n)={\prod }_{i=1}^n{p}_i$, then:

Consider the diagram given below and the following two statements:

Statement I: Regions X, Y and Z can be expressed as A ∩ B̅, A ∩ B and A̅ ∩ B respectively.. Statement II: P(Y) = P(A) – P(X) = P(B) – P(Z).

In the light of the above statements, choose the most appropriate answer from the options given below:

Statement I: If A ⊂ B; then B can be expressed as B = A ∪ (Ā ∩ B) and P(A) > P(B).

Statement II: $A\text{ and }B\text{ are independent events, then }(\bar{A}\text{ and }\bar{B}),(\bar{A}\text{ and }B)\text{ and }(A\text{ and }\bar{B})\text{ are also independent.}$

In the light of the above statements, choose the most appropriate answer from the options given below:

If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black balls will be drawn is

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: An elevator starts with m passengers and stops at n floors (m ≤ n). The probability that no passengers alight at the same floor is $P_{\text{Rm}}=\frac{m!}{n^m}$. Reason R: If (n+1) is an integer, say m, then P (x = r) = $n\cdot C_r\cdot p^r\cdot (1-p{)}^{n-r}$ is maximum when r = m or r = m-1

In the light of above statements, choose the most appropriate answer from the options given below: