Question

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?

Answer 1

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 (`0.28`). Staying unhurt is then `1-0.28=0.72`.

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.