List of top Mathematics Questions on Probability asked in WBJEE

Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and Ek={(a,b)∈S:ab=k}. If Pk=P(Ek), then the correct among the following is 
Let A and B be two independent events. The probability that both A and B happens is \(\frac{1}{12}\) and the probability that neither A nor B happens is \(\frac{1}{2}\). Then
$A$ and $B$ each select one number at random from the distinct numbers $1, 2, 3,.....,n$ and the probability that the number selected by $A$ is less than the number selected by $B$ is $\frac{1009}{2019}$ .Now , the probability that the number selected by $B$ is the number immediately next to the number selected by $A$ is
There are 7 greetings cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective colour is,
The probability that a non leap year selected at random will have $53$ Sundays is
If $A, B$ are two events such that $P\left(A\cup B\right) \ge \frac{3}{4}$ and $\frac{1}{8}\le P\left(A\cap B\right) \le\frac{3}{8}$ then
A fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is
A fair six-faced die is rolled $12$ times. The probability that each face turns up twice is equal to
An objective type test paper has $5$ questions. Out of these $5$ questions, $3$ questions have four options each $(A, B, C, D)$ with one option being the correct answer. The other $2$ questions have two options each, namely True and False. A candidate randomly ticks the options. Then the probability that he/she will tick the correct option in at least four questions, is
Let $A$ and $B$ be two events with $P\left(A^{c}\right)=0.3, P\left(B\right)=0.4$ and $P\left(A\cap B^{c}\right)=0.5$ Then $P\left(B|A \cup B^{c} \right) $ is equal to
An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then the probability that balls of both colours are drawn is
$A$ and $B$ are two independent events such that $P\left(A\cup B'\right)=0.8$, and $P\left(A\right)=0.3$ Then, $P(B)$ is
Directions: The following question has four choices, out of which one or more are correct.When photons of energy 4.25 eV strike the surface of a metal A, the ejected photoelectrons have minimum kinetic energy TA expressed in eV and de Broglie wavelength λA. The maximum kinetic energy ofphotoelectrons liberated from another metal B by photons of energy 4.70 eV is TB=(TA−1.50eV). If the de Broglie wavelength of these photoelectrons is λB=2λA, then
The value of cos 15° – sin 15° is
The value of cot−1⁡9+cos⁡ec−1414