Practice Questions on Binomial Distribution

Q1: If a coin is tossed 5 times find the probability of getting at most 2 heads.

Q2: A pair of dice is thrown 7 times. If getting a total of 11 is considered as a success, what is the probability of getting at least 3 success.

Q3: If mean of the binomial distribution is 20 and the number of observations is 30. Find the variance and standard deviation.

Q4: Find the mean of the binomial distribution given that number of trials is 80 and probability of success is 0.45.

Q5: Calculate the variance of the binomial distribution given that number of trials is 200 and probability of success is 0.8.

Q6: If the mean and variance of binomial distribution are 45 and 30. Find the binomial distribution.

Q7: The mean and variance of a binomial distribution are 6 and 2 then find P(X>3).

Q8: The probability of a boy hitting a target is 0.2. How Many times must he fire so that the probability of his hitting the target at least once is greater than 2/3.

Q9: Find the probability distribution of the number of heads when 5 coins are tossed.

Q10: There are 20 machine and that the chance of any one of them to be out of service is 0.025. Determine the probability that exactly three machines will be out of service on the same day.

Binomial Distribution is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, where each trial has only two possible outcomes: success or failure.

Imagine you’re flipping a coin, but not just once – you’re flipping it many times. Each time, you’re either getting heads or tails. The binomial distribution helps us figure out the chances of getting a certain number of heads (or tails) after flipping the coin a bunch of times.

Here are a few examples of situations that can be modelled using the binomial distribution:

• Suppose you flip a fair coin 10 times. Each flip is an independent trial, and there are only two possible outcomes: heads or tails.
• In a clinical trial, patients are often given a treatment or a placebo. The outcome for each patient might be success (the treatment works) or failure (the treatment doesn’t work).
• A factory produces a large number of items, and each item may be defective or non-defective. Inspectors randomly select a sample of items and check them for defects.
• In an election where voters can choose between two candidates, each voter’s decision can be seen as a trial with two possible outcomes: voting for Candidate A or voting for Candidate B.