Can you teach me how to do this problem? Thanks

Question

According to a survey, 45% of people carry at least 1 reusable water bottle. If 5 people are selected randomly, what is the probability that at least 3 of them will be carrying a reusable water bottle? Round your answer to the nearest tenth of a percent.

Answer 1

Study BINOMIAL DISTRIBUTION.

 

P(at least 3 carry reusable water bottle) = the sum of those terms of (0.45+0.55)⁵

where only the terms having 0.45 exponentiated to the powers 3, 4 and 5 are added.

 

These terms, added, give you the desired probability:

5C3•0.45³ •0.55²+ 5C4•0.45⁴ •0.55+ 5C5•0.45⁵ 

 

I let you do the computation. Don't do any rounding until the very end.