one treatment for smoking has a 60% success rate in helping people stop smoking. Suppose a group of 8 smokers are using this treatment

Question

What is the probability that more than 3 of them successfully stop smoking?

Answer 1

Hi Ricardo,

 

If we assume that each person's success is an independent event and that the success rate is constant at 0.6 for each person, then this defines a binomial experiment. In a binomial experiment, the random variable X is the number of successes in N trials given a constant probability p of success.

 

Here, we want the probability that X > 3. The easiest way to find this probability is to compute the probability of its complement, i.e, the probability that that 3 or fewer people are successful, and that probability from 1. We can do that in Excel using the BINOM.DIST(number_s, trials, probability_s, cumulative) function in Excel, where the arguments to the function are number_s, which is the number of successes X we want to look at , 3 here, trials is the number of trials of the experiment, 8 here (one trial for each person), probability_s is the probability of success, 0.6 here, and cumulative is true if we want the cumulative distribution, which is the probability of X or fewer successes, and FALSE if we want the probability  distribution (i.e., the probability of exactly X successes.

 

So in Excel paste the function

 

"=1-BINOM.DIST(3,8,0.6,TRUE)"

 

to obtain the answer 0.8263296. That is, the probability of 3 or fewer successes in 8 trials is 0.1736704, and since that event is the complement of more than 3 successes, the probability 0.8263296 = 1 - 0.1736704 is the answer.

 

Hope this helps, feel free to ask questions.

 

Kind regards,

Hugh