a binomial probability experiment is conducted

Question

a binomial probability experiment is conducted with the given parameters. compute the probability of x successes in the n independent trials of the experiment. 

n=13 p=0.35 x≤4

Answer 1

The binomial probability formula can be used to find the probability of a binomial experiment for a specific number of successes.  It DOES NOT find the probability for a RANGE of successes, as in this case.

 

The RANGE "x≤4" means x=0 OR x=1 OR x=2 OR x=3 OR x=4, so there are five different probability calculations to do.

 

In order to find the total probability we use the addition rule that states that the probabilities of different events can be added to find the probability for the entire set of events only if the events are MUTUALLY EXCLUSIVE. The outcomes of a binomial experiment are mutually exclusive for any value of x between zero and n, as long as n and p don't change, so we're allowed to add the five calculated probabilities together to find the total probability.

 

The probability that x≤4 can be written as P(X≤4) or as P(X=0 or X=1 or X=2 or X=3 or X=4) which means (because of the addition rule) that P(x≤4) = P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4)

 

If you have any questions about using the binomial probability formula to calculate a probability for specific values of n, p, and x please post a separate question or contact me directly!