National Council of Examiners for Engineering and Surveying (NCEES) Fundamentals of Engineering (FE) Industrial and Systems Practice Exam

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What is the probability of getting exactly four heads when tossing a fair coin ten times?

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To determine the probability of getting exactly four heads when tossing a fair coin ten times, we use the binomial probability formula, which is expressed as:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

where:

- \( n \) is the number of trials (in this case, 10 coin tosses),

- \( k \) is the number of successful outcomes we are interested in (four heads),

- \( p \) is the probability of success on an individual trial (for a fair coin, \( p = 0.5 \)),

- \( \binom{n}{k} \) represents the binomial coefficient, calculated as \( \frac{n!}{k!(n-k)!} \).

1. **Calculate the binomial coefficient** \(\binom{10}{4}\):

\[

\binom{10}{4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times

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