Gundersons should be careful

From the given, the probability that Mr. Gunderson doesn't have an accident is $1-0.02 = 0.98$ .

The probability that Mrs. Gunderson doesn't have an accident is $1-0.015 = 0.985$ .

Then the probability that they both don't have any accidents is just the product of the individual probabilities, i.e. $(0.985)(0.98)=0.9653$

Our answer is the complement of this, i.e. $1-0.9653 = 0.0347$ .

Relevant wiki: Probabilistic Principle of Inclusion and Exclusion

Let $A$ be the event that Mr. Gunderson has an accident, and let $B$ be the event that Mrs. Gunderson has an accident. It is given that $P(A)=0.02$ and $P(B)=0.015$ .

$A$ and $B$ are independent. By the rule of product , $P(A\cap B)=P(A)\times P(B)=0.0003$ .

The problem is asking for $P(A\cup B)$ .

Using the PPIE, this is:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)=\boxed{0.0347}$ .