A coffee shop owner knows from past records that 20 of all c

A coffee shop owner knows from past records that 20% of all customers who enter her store will buy a danish. if 10 people enter the store what is the probability that no one buys a danish?

How many people must enter the store before she is 85% sure that at least one person will buy something?

Solution

prob of people buying danish = 0.20

p = 0.20

n = 10

X no of people buying Danish is binomial with p =0.20

the probability that no one buys a danish

= P(X=0) = 0.80¹⁰

⁼ 0.1074

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If N is the no of people enter for her to be 85% confidence

for atleast one person buying Danish

= P(X>=1 in N trials)

= 1-P(X=0 in N trials) =0.85

i.e. P(X=0) = 0.15

x = 8 persons is the answer