# The probability that John falls off a ladder and breaks his arm is 0.2, and the probability that John falls off a ladder and breaks his leg is .08. Are these events mutually exclusive (disjoint)? Why or why not?

##### 1 Answer

Feb 6, 2015

This is a tricky one. Much depends on the exact wording of the question.

If you see the words **either...or** the two possibilities are mutually exclusive, and then you may add the chances of John breaking a limb (

If not, there are four possible events

- he does not break anything
- he breaks an arm
- he breaks a leg
- he breaks both an arm and a leg

(In real life he could or could not break one or two arms and/or legs in any combination, but that doesn't count in this question.)

Calculation of possibilities is more complicated in this situation.

I would advise you to use a chance-tree or a two-way table.