A congested computer network has a 0.002 probability of losinga data packet and packet losses are independent events. Alost packet must be resent.
a) What is the probability that an e-mail message with100 packets will need any resent?
b) What is the probability that an e-mail message with 3packets will need exactly one to be resent?
c) If 10 e-mail messages are sent, each with 100packets, what is that probability that at least one message willneed some packets to be resent?

i know the answer for (a) is P= 1-(1-0.002)^100

however i need some help understanding why it is so. i know the (1-0.002) is the probability that a packet is not lost. i also know that since there are 100 packets in the e-mail, that there are x^100 chances of it not being lost.

i do not understand why (1-0.002)^100 is subtracted from 1, wouldn't this give the probability that ALL are lost?

also, why can't you just do (probability packets lost)^100?, (0.002)^100,a and how about (b) and (c)?