Question

Ashley‘s Internet service is terribly unreliable in fact on any given day there’s a 60% chance that her Internet‘s connection will be lost at some point that day what is the probability that her Internet service is not broken for seven days in a row inner a fraction or round your answer to four decimal places if necessary.

Answer 1

Let the event that her internet will be broken be A

The event that her internet will not be broken be B

Therefore:

`\begin{gathered} P(A)=60\%=0.60 \\ P(B)=1-0.60=0.4 \end{gathered}`

Thus, the probability that her internet is not broken for 7 days in a row:

`P(B\text{ for 7 days\rparen=P\lparen B\rparen}*\text{P\lparen B\rparen}*\text{P\lparen B\rparen}*\text{P\lparen B\rparen}*\text{P\lparen B\rparen}*\text{P\lparen B\rparen}*\text{P\lparen B\rparen}`

Substitute the value:

`P(B\text{ for 7 days\rparen=0.4}*\text{0.4}*\text{0.4}*\text{0.4}*\text{0.4}*\text{0.4}*\text{0.4=0.001634}`

Round to four decimal places is 0.0016

Answer: 0.0016