How often will a die come up "4"? How likely is it to rain tomorrow? Probability is one of the most powerful frameworks for modeling the world around us.

Suppose you flip a fair coin (i.e., a coin that lands Heads with probability 1/2 and Tails with probability 1/2) 4 times. Which of these outcomes is most likely?

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Suppose you flip a fair coin (i.e., a coin that lands Heads with probability 1/2 and Tails with probability 1/2) 4 times. Which of these sequences of Heads (H) and Tails (T) is most likely?

Excel in math and science

Master concepts by solving fun, challenging problems.

It’s hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!

Suppose you flip a fair coin (i.e., a coin that lands Heads with probability 1/2 and Tails with probability 1/2) 10 times. Which of these sequences of Heads (H) and Tails (T) is most likely?

Excel in math and science

Master concepts by solving fun, challenging problems.

It’s hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!