Suppose the percentage of drinks sold from a vending machine

Suppose the percentage of drinks sold from a vending machine are 80% and 20% for soft drinks and bottled water, respectively. What is the probability that on a randomly selected day, the first soft drink is the fourth drink sold? Find the probability that exactly 1 out of 10 drinks sold is a soft drink. Find the probability that the fifth soft drink is the seventh drink sold. Verify empirically that P(Bin(n, pi)

Solution

21)
P(Sold for vending macchine) = 0.80
P(Soft drinks ) = 0.20
a)
Among four drinnk sold fourth is soft drinks = 0.80*0.80*0.80*0.20 = 0.1024
b)
P( X = 1 ) = ( 10 1 ) * ( 0.2^1) * ( 1 - 0.2 )^9
= 0.2684