In a communication network, messages are received one at a time and checked for errors. It is known that 6% of messages have an error in them. Errors in one message are independent of errors in any other message. li) Find the probability that the first message that contains an error is the fifth message to be checked. (ii) Find the mean number of messages before the first that contains an error is found. (iii) Find the probability that there are no errors in the first ten messages. (iv) Find the most likely number of messages to be checked to find the first that contains an error.

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6.6
In a communication network, messages are received one at a time and
checked for errors. It is known that 6% of messages have an error in them.
Errors in one message are independent of errors in
any
other
message.
(i)
Find the probability that the first message that contains an error is the
fifth message to be checked.
(ii) Find the mean number of messages before the first that contains an
error is found.
(iii) Find the probability that there are no errors in the first ten messages.
(iv) Find the most likely number of messages to be checked to find the first
that contains an error.
Transcribed Image Text:6.6 In a communication network, messages are received one at a time and checked for errors. It is known that 6% of messages have an error in them. Errors in one message are independent of errors in any other message. (i) Find the probability that the first message that contains an error is the fifth message to be checked. (ii) Find the mean number of messages before the first that contains an error is found. (iii) Find the probability that there are no errors in the first ten messages. (iv) Find the most likely number of messages to be checked to find the first that contains an error.
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