John emailed 128 people to invite them to the restaurant's inauguration party. He asked these guests to send the email to 5 others in exchange for participation in a lottery where a free meal for two is won. Based on the assumptions made below, how many of those who received the email are expected to come to the party?
Assumptions •half of the 128 people emailed the other 5. •1/4 of these sent the email to 5 others. •1/8 of these sent the email to 5 others •1/16 of these sent the email to 5 others. • No one received the email more than once. • 10% of those who received the email will go to the party.
All help/ solutions appreciated!
See my answer at: this equivalent question
(copy-paste)
Not sure if this is the answer to some kind of test you need to make...
But note that in 'step' 1, 128 people receive an email. For step 2, we have that out of these 128 persons, 1/2 forwarded it to 5 people, hence #persons receiving an email = $(\tfrac{1}{2}*128)*5$. For the third step, we have that out of these $(\tfrac{1}{2}*128)*5$ people, 1/4th forwards this to 5 new persons, i.e. the number of individuals receiving this email is: $\left(\tfrac{1}{4}\left[(\tfrac{1}{2}*128)*5\right]\right)*5$, and so forth to the $n$th step. Thus we can describe the number of people actually receiving the email with $$\sum_{i=0}^n \frac{128\cdot 5^i}{2^{(\sum_{j=0}^i j )}}.$$ With $n$ the 'step' number. Your answer is 10% of the above with $n=4$.
(this results in percentages of persons btw)