Question

question 3 1 points 34% of ua students are known to use macbooks. 72% are known to use iphones. assume the probability of intersection is 29%. a student is selected at random and questioned about their technology usage. what is the probability of the student using an iphone and not a macbook? 72% 29% 34% 43%

Explanation:

Step1: Use the formula for probability of intersection and complements

Let $A$ be the event of using an iPhone and $B$ be the event of using a MacBook. We know $P(A) = 0.72$, $P(B)=0.34$, and $P(A\cap B)=0.29$. We want to find $P(A\cap\overline{B})$.
We know that $P(A)=P(A\cap B)+P(A\cap\overline{B})$ (since $A=(A\cap B)\cup(A\cap\overline{B})$ and $(A\cap B)\cap(A\cap\overline{B})=\varnothing$).

Step2: Solve for $P(A\cap\overline{B})$

Rearrange the formula: $P(A\cap\overline{B})=P(A)-P(A\cap B)$.
Substitute the given values: $P(A\cap\overline{B}) = 0.72 - 0.29$.
$P(A\cap\overline{B})=0.43$.

Answer:

43%