independent events

Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) _________...

The probability of getting a ''head'' in a single toss of a biased coin is $$0.3.$$ The coin is tossed repeatedly till a ''head'' is obtained. If the tosses are independent, then t...

Let $$\,\,X \in \left\{ {0,1} \right\}\,\,$$ and $$\,\,Y \in \left\{ {0,1} \right\}\,\,$$ be two independent binary random variables. If $$\,\,P\left( {X\,\, = 0} \right) = p\,\,$$...

Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability that...

Let $$X \in \left\{ {0,1} \right\}$$ and $$Y \in \left\{ {0,1} \right\}$$ be two independent binary random variables. If $$P\left( {X\,\, = 0} \right)\,\, = p$$ and $$P\left( {Y\,\...

Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is $$1/6$$ and that of Ramesh is $$1/8$$. What is the probabili...

Suppose $$A$$ & $$B$$ are two independent events with probabilities $$P\left( A \right) \ne 0$$ and $$P\left( B \right) \ne 0.$$ Let $$\overrightarrow A $$ & $$\overrightarrow B $$...

A fair coin is tossed $$10$$ times. What is the probability that only the first two tosses will yield heads?

A fair dice is rolled twice. The probability that an odd number will follow an even number is

During transmission over a communication channel, bit errors occur independently with probability 'p'. If a block of n bits is transmitted, the probability of at most one bit error...

In a digital communication system, transmissions of successive bits through a noisy channel are assumed to be independent events with error probability p. The probability of at mos...