Question 11.7.E.35: Using the percents as probabilities, find the probability th...
Using the percents as probabilities, find the probability that, out of 10 states selected at random, the following are true.
Fewer than 2 states have 8 or more representatives.
This can be considered as a binomial experiment with n = 10 and success as “select a state that has 8 or more representatives.” Therefore
p = P(success) = 0.28 + 0.14 = 0.42,
and q = P(failure) = 1 – 0.42 = 0.58.
“Fewer than 2” means that either 0 states or 1 state in the sample have 8 or more representatives. The probability, then, is
\left(\begin{matrix}10\\0 \end{matrix} \right) (0.42)^{0}(0.58)^{10} + \left(\begin{matrix} 10\\1 \end{matrix} \right) (0.42)^{1}(0.58)^{9} ≈ 0.036.Related Answered Questions
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