State True or False for the statements: Two independent events ar… - Vidyadip

Question

State True or False for the statements:
Two independent events are always mutually exclusive.

✓

Answer

False.
Explanation:
No, mutually exclusive events (with non-zero probability) are always dependent. The definition of independence for events A and B is that P(A and B) ... However, in the case that A and B are mutually exclusive, then P(A and B) = 0.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "True False[1 Marks ]" from Probability→Probability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Which of the following statements are True or False.
Matrix multiplication is commutative.

State True or False for the following:
The angle between the line $\vec{\text{r}}=(5\hat{\text{i}}-\hat{\text{j}}-4\hat{\text{k}})+\lambda(2\hat{\text{i}}-\hat{\text{j}}-\hat{\text{k}})$ and the plane $\vec{\text{r}}(3\hat{\text{i}}-4\hat{\text{j}}-\hat{\text{k}})+5=0$ is $\sin^{-1}\Big(\frac{5}{2\sqrt{91}}\Big).$

Which of the following statements are True or False.
If A and B are two square matrices of the same order, then A + B = B + A.

State True or False for the following:
If the foot of perpendicular drawn from the origin to a plane is (5, -3, -2), then the equation of plane is $\vec{\text{r}}\cdot(5\hat{\text{i}}-3\hat{\text{j}}-2\hat{\text{k}})=38.$

Which of the following statements are True or False.
If A and B are two matrices of the same order, then A - B = B - A.

Which of the following statements are True or False.
If matrix AB = 0, then A = 0 or B = 0 or both A and B are null matrices.

State True or False for the statements of the following Exercise:
If the determinant $\begin{vmatrix}\text{x}+\text{a}&\text{p}+\text{u}&\text{l}+\text{f}\\\text{y}+\text{b}&\text{q}+\text{v}&\text{m}+\text{g}\\\text{z}+\text{c}&\text{r}+\text{w}&\text{n}+\text{h}\end{vmatrix}$ splits into exactly K determinants of order 3, each element of which contains only one term, then the value of K is 8.

State whether the statements are True or False:
In a LPP, the minimum value of the objective function Z = ax + by is always 0 if origin is one of the corner point of the feasible region.

State True or False for the statements of the following Exercise:
$\big(\text{A}^3\big)^{-1}=(\text{A}^{-1})^3,$ where A is square matrx and |A| ≠ 0.

State True or False for the statements:
If A and B are mutually exclusive events, then they will be independent also.