Drug math problum help!

[desi43]

20% of all people affected with a rare disease will recover. A new vaccine is developed and tested on 20 people selected at random with the disease. 18 of the 20 people recover. what is the probability that exactly 18 people recover without taking the vaccine?

i am really lost on this problem i know it requires binomial's. so far i have


C (20,18) (0.20^18) + 1(0.20^20)

but i am not sure if this is right. can someone please help?


thank you so much!

 

[pka]

It should be: \(\displaystyle \L
C(20,18)\left( {.2} \right)^{18} (.8)^2\)