Answer
$0.1653$
Work Step by Step
According to Bayes' theorem:
$P(S|D)=\dfrac{P(D|S)P(S)}{P(D|S)P(S)+P(D|C)+P(C)+P(D|L)P(L)}~~~~~~~~(1)$
Here, we have
$P(C)= 45.4 \% =0.454\\ P(S)= 27.3 \% =0.273 \\ P(L)=27.3 \%=0.273\\P(D|C)= 1 \\ P(D|S)=0.371\\ P(D|L)=0.210\\$
Now, we will now use formula (1) and the given data to obtain:
$P(S|D)=\dfrac{P(D|S)P(S)}{P(D|S)P(S)+P(D|C)+P(C)+P(D|L)P(L)}=\dfrac{(0.371)(0.273)}{(0.371)(0.273)+(1)(0.454)+0.210(0.273)}$
or, $ \approx 0.1653$
Thus, we conclude the probability that the victim of a deadly side-impact accident was driving an SUV is approximately $0.1653$.
