Probability Theory Practice Questions

A. There is a sample point at which X has the value 5.

B. There is a sample point at which X has value greater than 5.

C. There is a sample point at which X has a value greater than equal to 5.

D. None of the above

A. $P_r[E_1\: \text{or} \:E_2] \text{ is } \frac{2}{3}$

B. Events $E_1$ and $E_2$ are independent

C. Events $E_1$ and $E_2$ are not independent

D. $P_r \left[{E_1}\mid{E_2} \right] = \frac{4}{5}$

A. $\dfrac{1}{6}$

B. $\dfrac{3}{8}$

C. $\dfrac{1}{8}$

D. $\dfrac{1}{2}$

A. 0.3

B. 0.25

C. 0.35

D. 0.4

A. $\frac{4}{52} \times \frac{4}{52}$

B. $\frac{4}{52} \times \frac{3}{52}$

C. $\frac{4}{52} \times \frac{3}{51}$

D. $\frac{4}{52} \times \frac{4}{51}$

A. $\frac{1}{36}$

B. $\frac{1}{3}$

C. $\frac{25}{36}$

D. $\frac{11}{36}$

A. $\dfrac{16}{25}$

B. $\left(\dfrac{9}{10}\right)^{3}$

C. $\dfrac{27}{75}$

D. $\dfrac{18}{25}$

A. $\frac{2}{3}$

B. $\frac{4}{5}$

C. $\frac{1}{2}$

D. $\frac{1}{3}$

A. $P (A \cap B) = P(A)P(B)$

B. $P (A \cup B) = P(A)+P(B)$

C. $P (A \mid B) = P(A \cap B)P(B)$

D. $P (A \cup B) \leq P(A) + P(B)$

A. For poisson distribution, the mean is twice the variance.

B. In queuing theory, if arrivals occur according to poisson distribution, then the inter-arrival time is exponentially distributed.

C. The distribution of waiting time is independent of the service discipline used in selecting the waiting customers for service.

D. If the time between successive arrivals is exponential, then the time between the occurences of every third arrival is also exponential.