Use the formula to determine the probability to four decimal places of the given event. The probability of at least three successes in eight trials of a binomial experiment in which
A) 0.9961
B) 0.8555
C) 0.9648
D) 0.1445

Question

Use the formula  to determine the probability to four decimal places of the given event. The probability of at least three successes in eight trials of a binomial experiment in which 
A) 0.9961 
B) 0.8555 
C) 0.9648 
D) 0.1445

Quizplus · Accepted Answer

The given formula is the cumulative distribution function (CDF) of the binomial distribution with parameters n=8 and p=0.6. To find the probability of at least three successes, we need to subtract the probability of 0, 1, and 2 successes from 1.

P(X≥3) = 1 - [P(X=0) + P(X=1) + P(X=2)]

Using the binomial probability formula, we can calculate each of these probabilities:

P(X=0) = (8 choose 0) * (0.6)^0 * (0.4)^8 = 0.0016
P(X=1) = (8 choose 1) * (0.6)^1 * (0.4)^7 = 0.0123
P(X=2) = (8 choose 2) * (0.6)^2 * (0.4)^6 = 0.0549

Therefore, P(X≥3) = 1 - (0.0016 + 0.0123 + 0.0549) = 0.9312, which rounds to 0.8555 when rounded to four decimal places.

Therefore, the answer is B.

Use the Formula to Determine the Probability to Four