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For the San Jose Sharks example, X ~ B(12, 0.3694) counts wins in 12 games. Using the binomial formula, what is P(x=6), the probability of exactly six wins?
A0.1476
B0.2336
C0.7664
D0.8903
Answer & Solution
Correct answer: A. 0.1476
1. The binomial formula is P(X=x) = C(n,x) p^x q^(n-x), here with n=12, p=0.3694, x=6.
2. C(12,6) = 924, and (0.3694)^6 (0.6306)^6 combine with that count to give the probability.
3. Evaluating this gives P(x=6) ≈ 0.1476.
4. Options B, C, and D are the values for other events in this same problem set, not P(x=6) itself.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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