What’s the prob that more than 12 of the next 20 customers entering the cinema have bought a ticket online?

Taz: What’s the prob that more than 12 of the next 20 customers entering the cinema have bought a ticket online?
According to statistics provided by a ticket office, 20% of movie tickets are purchased online. What is the probability that more than twelve of the next 20 customers entering the cinema have bought a ticket online?Justify that this can be modelled using the binomial distribution by showing whether or not the necessary conditions hold. Show working.

Answers and Views:

Answer by freond1
Look at the (.2 + .8 )^20
This gives you the distribution.
Probability that 20 were purchased online is .2^20 x .8^0 x 20C20
Probability that 19 were purchased online is .2^19 x .8^1 x 20C19
….
Probability that 13 were purchased online is .2^13 x .8^7 x 20C13

The sum of these is the probability that more than 12 were purchased online.

https://en.wikipedia.org/wiki/Binomial_distribution might help with the rest of it–necessary conditions, etc.