1
WB JEE 2023
+1
-0.25 Let A and B are two independent events. The probability that both A and B happen is $${1 \over {12}}$$ and probability that neither A and B happen is $${1 \over 2}$$. Then

A
$$P(A) = {1 \over 3},P(B) = {1 \over 4}$$
B
$$P(A) = {1 \over 2},P(B) = {1 \over 6}$$
C
$$P(A) = {1 \over 6},P(B) = {1 \over 2}$$
D
$$P(A) = {2 \over 3},P(B) = {1 \over 8}$$
2
WB JEE 2023
+1
-0.25 Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and $$\mathrm{E_k=\{(a,b)\in S:ab=k\}}$$. If $$\mathrm{p_k=P(E_k)}$$, then the correct among the following is :

A
$$\mathrm{p_1 < p_{10} < p_4}$$
B
$$\mathrm{p_1 < p_{8} < p_{14}}$$
C
$$\mathrm{p_1 < p_{8} < p_{17}}$$
D
$$\mathrm{p_1 < p_{16} < p_5}$$
3
WB JEE 2022
+1
-0.25 A, B, C are mutually exclusive events such that $$P(A) = {{3x + 1} \over 3}$$, $$P(B) = {{1 - x} \over 4}$$ and $$P(C) = {{1 - 2x} \over 2}$$. Then the set of possible values of x are in

A
[0, 1]
B
$$\left[ {{1 \over 3},{1 \over 2}} \right]$$
C
$$\left[ {{1 \over 3},{2 \over 3}} \right]$$
D
$$\left[ {{1 \over 3},{{13} \over 3}} \right]$$
4
WB JEE 2022
+1
-0.25 A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is

A
$${3 \over {16}}$$
B
$${3 \over 8}$$
C
$${1 \over 4}$$
D
$${5 \over 8}$$
WB JEE Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
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