encounter infected

Question

The CDC estimates that a non-infected person has a  .10 chance of contracting mumps from an infected person from even a brief encounter. What is the probability that a non-infected person contracts mumps after  8 brief encounters with infected people?

Answer 1

Ue Bernoulli formula

(N!)/(n!*(N-n)!)*pⁿ*q^N-n

N is the total number of occurrences

n is number of times an event happened

p is probability that an event happened

q or 1-p is probability that event did not happen

Factorial formula tells number of possible ways for event to happen (first, second, third,..)

For this problem, infection needs to happen once.

n=1.

# ways for event to happen is 8!/(1!*7!) or 8.

p=0.10, q is 1-0.10 or 0.9

P( infection)=8*(.10)¹*(0.9)⁷

P=0.38