Exercise · ZW-BINOMIAL-DISTRIBUTION-009 · ★★★ Advanced
If \(X\) is binomial with \(n=10\) and \(p=\tfrac12\), which probability equals \(P(X=3)\)?
Choose one option.
Show answer
- C. \(P(X=7)\)
Explanation
With \(p=\tfrac12\) the distribution is symmetric: \(\binom{10}{3}=\binom{10}{7}=120\) and the power of \(\tfrac12\) is the same, \(2^{-10}\), in both cases.
Review the concept: Binomial distribution
A binomial variable \(X\) counts the successes \(k\) in \(n\) independent Bernoulli trials with the same success probability \(p\); \(P(X=k)\) is the probability of getting \(k\) successes.
\[P(X=k)=\binom{n}{k}p^{k}(1-p)^{n-k},\quad k=0,1,\dots,n\]
More practice problems: binomial distribution
- ZW-BINOMIAL-DISTRIBUTION-001 A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads?
- ZW-BINOMIAL-DISTRIBUTION-002 If X is binomial with n=20 and p=0.3, compute E[X].
- ZW-BINOMIAL-DISTRIBUTION-003 If X is binomial with n=20 and p=0.3, compute Var(X).
- ZW-BINOMIAL-DISTRIBUTION-004 A binomial variable has n=10 and p=0.1. What is P(X=0), rounded to 4 decimals?
- ZW-BINOMIAL-DISTRIBUTION-005 In which situation is the random variable binomial?
- ZW-BINOMIAL-DISTRIBUTION-006 A fair coin is tossed 3 times. What is the probability of getting at least one head?
- ZW-BINOMIAL-DISTRIBUTION-007 A die is rolled 6 times. What is the probability of getting exactly one 6?
- ZW-BINOMIAL-DISTRIBUTION-008 A binomial variable has mean 12 and variance 3. What are n and p?
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