Practice Binomial Distribution – Complete Detail - 18.X | 18. Binomial Distribution | Mathematics - iii (Differential Calculus) - Vol 3
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Binomial Distribution – Complete Detail

18.X - Binomial Distribution – Complete Detail

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the probability of getting exactly 1 head when you flip a fair coin twice?

💡 Hint: Use the PMF formula for n=2, k=1, and p=0.5.

Question 2 Easy

If a die is rolled 3 times, what is the probability of getting exactly 2 sixes?

💡 Hint: Recognize there are 3 ways to choose which roll is not a six.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for the probability mass function of the Binomial Distribution?

P(X = k) = (n choose k) * p^(n-k) * (1-p)^k
P(X = k) = (n-k choose k) * p^k * (1-p)^n
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

💡 Hint: Remember the arrangement of p and (1-p) with respect to k and n.

Question 2

The mean of a binomial distribution is calculated as which of the following?

E(X) = n(1 - p)
E(X) = np
E(X) = p/n

💡 Hint: Think about how the average number of successes is determined.

3 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

A biased coin shows a 60% chance of landing heads. If flipped 10 times, what is the probability of getting exactly 6 heads?

💡 Hint: Calculate the binomial coefficient and powers separately.

Challenge 2 Hard

In a shipment of 100 items, 90% are defect-free. If 15 items are chosen at random, compute the probability that at least 12 will be defect-free.

💡 Hint: Consider using a cumulative approach for summation.

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