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:

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