Probability and Statistics

A fair six-sided die is rolled once. What is the probability of getting an even number?

In a class of 40 students, 25 like cricket, 18 like football, and 10 like both. How many students like neither cricket nor football?

If two coins are tossed simultaneously, what is the probability of getting at least one head?

A box contains 5 red, 7 blue, and 8 green balls. One ball is drawn at random. What is the probability that the ball is neither red nor green?

The mean of 10 observations is 20. If one observation 25 is replaced by 30, what is the new mean?

The variance of a data set is 16. What is the standard deviation?

If the probability of an event occurring is 0.7, what is the probability that it does not occur?

A random variable X has the probability distribution: P(X=1)=0.2, P(X=2)=0.5, P(X=3)=0.3. What is the expected value E(X)?

In a normal distribution, approximately what percentage of data lies within one standard deviation from the mean?

From a group of 5 men and 7 women, a committee of 4 is to be formed such that at least 2 women are included. How many such committees are possible?