What is the probability of obtaining exactly 5 P events if the appropriate term of the binomial expansion to evaluate were 6 P 5 Q 1 and P = 0.42?
A) 0.0784
B) 0.0455
C) 0.4616
D) 0.0076

Question

Quizplus · Accepted Answer

The probability of obtaining exactly 5 P events in a binomial distribution is calculated using the formula for a specific term in the binomial expansion, which is: $ \binom{n}{k} p^k q^{n-k} $, where $ \binom{n}{k} $ is the binomial coefficient, $ p $ is the probability of success (P event), $ q $ is the probability of failure (Q event), $ n $ is the total number of events, and $ k $ is the number of successful events. Given $ n = 6 $, $ k = 5 $, $ p = 0.42 $, and $ q = 1 - p = 0.58 $, the term is $ \binom{6}{5} (0.42)^5 (0.58)^1 $. Calculating this gives a probability of approximately 0.0455.

What Is the Probability of Obtaining Exactly 5 P Events