The probability that an event will happen is P(E)=14-17. Find the probability that the event will not happen.

Answer 1

You know that an event will either happen or not. So the probability of the event happening, P(E), and the probability of the event not happening, P(not E) is the whole game i.e. 100% or 1. So P(E)+P(not E)=1. We want to find P(not E) so we will leave that on the left and move everything else to the right of the equal sign (don;t forget to flip signs!) to get

P(not E)=1-P(E)

Now we know that P(E)=14/17 therefore P(not E)=1-14/17=3/17.

Another way to think of this problem is this:

You know that P(E)=14/17. That means that out of 17 tries, 14 times E will happen. What about the remaining times? Well E won't happen. How many times are left? 17-14=3.

So P(not E)=# of times E does not happen/total # of tries =3/17.