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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Which of the following statements are True or False.
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

State True or False for the following:
Differential equation representing the family of curves $\text{y}=\text{e}^{\text{x}}(\text{A}\cos\text{x}+\text{B}\sin\text{x})$ is $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}-2\frac{\text{dy}}{\text{dx}}+2\text{y}=0.$

State True or False for the following:
The solution of $\frac{\text{dy}}{\text{dx}}=\Big(\frac{\text{y}}{\text{x}}\Big)^{\frac{1}{3}}$ is $\text{y}^{\frac{2}{3}}-\text{x}^{\frac{2}{3}}=\text{C}.$

State True or False for the statements:
Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.

State True or False for the following:
The solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}+2\text{y}}{\text{x}}$ is $\text{x}+\text{y}=\text{k}\text{x}^2.$

State True or False for the statements of the following Exercise:
If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.

State True or False for the following:
The angle between the planes $\vec{\text{r}}\cdot(2\hat{\text{i}}-3\hat{\text{j}}+\text{k})=1$ and $\vec{\text{r}}\cdot(\hat{\text{i}}-\hat{\text{j}})=4$ is $\cos^{-1}\Big(\frac{-5}{\sqrt{58}}\Big).$

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.

Which of the following statements are True or False.
If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Which of the following statements are True or False.If $\text{A}=\begin{bmatrix}2&3&-1\\1&4&2\end{bmatrix}$ and $\text{B}=\begin{bmatrix}2&3\\4&5\\2&1\end{bmatrix},$ then AB and BA are defined and equal.