# Is the contrapositive of "if the probability of an event is 0.1, then the event is unlikely to occur" true or false?The truth value of the contrapositive is the same as the conditional statement...

Is the contrapositive of "if the probability of an event is 0.1, then the event is unlikely to occur" true or false?

The truth value of the contrapositive is the same as the conditional statement stated above?

*print*Print*list*Cite

## Is the contrapositive of "if the probability of an event is 0.1, then the event is unlikely to occur" true or false?

The contrapositive of a conditional statement logically always has the same truth value as the conditional statement. Since the conditional statement is true (the probability *p* of an event is assigned a number `0<=p<=1` with 0 impossible and 1 guaranteed, so p=.1 is very unlikely), the contrapositive must also be true.

You would have to be careful in how you worded the contrapositive, as the statement "An event is likely to occur if the probability of the event is not .1" is false. A better wording might be an event is likely to occur if the probability of an event is .9. Here we use the fact that the negation of never is always, and the negation of addition is subtraction, so we replace 0+.1 with 1-.1.

So with careful wording the contrapositive is true.