Question

isaac is shopping for a new bicycle. he is most interested in color and type of tires. the probability that a bike is blue is 0.73, the probability that it has city bike tires is 0.64, and the probability that it is blue or has city bike tires is 0.8. what is the probability that a randomly chosen bike is blue and has city bike tires? write your answer as a whole number, decimal, or simplified fraction.

Explanation:

Step1: Recall the formula for the probability of the union

The formula for $P(A\cup B)$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event that the bike is blue and $B$ be the event that the bike has city - bike tires. We know that $P(A) = 0.73$, $P(B)=0.64$ and $P(A\cup B)=0.8$.

Step2: Rearrange the formula to solve for $P(A\cap B)$

We can rewrite the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ as $P(A\cap B)=P(A)+P(B)-P(A\cup B)$.

Step3: Substitute the given values

Substitute $P(A) = 0.73$, $P(B)=0.64$ and $P(A\cup B)=0.8$ into the formula: $P(A\cap B)=0.73 + 0.64-0.8$.
$P(A\cap B)=0.57$.

Answer:

$0.57$