The whole question: Ruth, the owner of a mail-order business, estimates that the probability that a household receiving one of her catalogs will place an order with her is .10. And then How many catalogs must Ruth send out to ensure that the chances of obtaining at least one order is 50% or better? Thanks in advance.
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The probably that at least 1 order is sent is equal to 1-[probability that NO orders are sent].
So let's say
P=1-(0.9)^n where n is the number of catalogs sent out. And we want P=0.5 at least. So
0.5=1-(0.9)^n
(0.9)^n=0.5
nlog(0.9)=log(0.5)
Re arrange this for n, and if n isn't an integer round up to the nearest one :)
So let's say
P=1-(0.9)^n where n is the number of catalogs sent out. And we want P=0.5 at least. So
0.5=1-(0.9)^n
(0.9)^n=0.5
nlog(0.9)=log(0.5)
Re arrange this for n, and if n isn't an integer round up to the nearest one :)