Question

on new years eve, the probability of a person driving while intoxicated or having an accident is 0.34. if the probability of driving while intoxicated is 0.31 and the probability of having a driving accident is 0.1, find the probability of a person having a driving accident while intoxicated.
the probability of a person having a driving accident while intoxicated is
(type an integer or a decimal.)

Explanation:

Step1: Recall the formula for the probability of the union of two events

Let $A$ be the event of driving while intoxicated and $B$ be the event of having a driving - accident. The formula is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.

Step2: Identify the given probabilities

We are given that $P(A\cup B) = 0.34$, $P(A)=0.31$, and $P(B)=0.1$.

Step3: Solve for $P(A\cap B)$

Substitute the given values into the formula: $0.34 = 0.31+0.1 - P(A\cap B)$.
First, simplify the right - hand side: $0.31 + 0.1=0.41$. So, the equation becomes $0.34=0.41 - P(A\cap B)$.
Then, solve for $P(A\cap B)$: $P(A\cap B)=0.41 - 0.34$.
$P(A\cap B)=0.07$.

Answer:

$0.07$