binomial distribution

A day can only be cloudy or sunny. The probability of a day being cloudy is 0.5 , independent of the condition on other days. What is the probability that in any given four days, t...

A fair six-faced dice, with the faces labelled ' 1 ', ' 2 ', ' 3 ', ' 4 ', ' 5 ', and ' 6 ', is rolled thrice. What is the probability of rolling ' 6 ' exactly once?

For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of...

A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?

For any discrete random variable $$X,$$ with probability mass function $$P\left( {X = j} \right) = {p_j},$$ $${p_j}\,\, \ge 0,\,j \in \left\{ {0,..........,\,\,\,N} \right\},$$ and...

For each elements in a set of size $$2n$$, an unbiased coin in tossed. The $$2n$$ coin tosses are independent. An element is chhoosen if the corresponding coin toss were head.The p...

If a fair coin is tossed four times, what is the probability that two heads and two tails will result?

A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is