Question

suppose it is known that 80% of the people exposed to the flu virus will contract the flu. out of a family of six exposed to the virus, what is the probability that no more than two will contract the flu?

Answer 1

Let X denote the random variable representing the number of people who will contract the flu out of the family of six exposed to the flu virus.

Now, since there is a fixed number of trials (fixed number of people), there are two outcomes (contracting the flu or not contracting the flu) and each family member contracts the flu with probability 80% = 0.8 independent of other family members, thus we can conclude that:

X ~ Binomial(n = 6, p = 0.8) and the probability mass function of X is given by:

Now, the probability that no more than two of the 6 family members will contract the flu is given by:

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.