Question

A town has two shopping malls. A survey conducted on the shopping preferences of the town's residents showed that 62% of the residents visit Comet Mall, 73% of the residents visit Star Mall, and 48% of the residents visit both malls.
The probability that a resident chosen at random shops at either Comet Mall or at Star Mall is
%.?
PLZ help what is the percent??

Answer 1

Given:

62% of the residents visit Comet Mall.

73% of the residents visit Star Mall.

48% of the residents visit both malls.

To find:

The probability that a resident chosen at random shops at either Comet Mall or at Star Mall.

Solution:

Let A be the event that the residents visit Comet Mall and B be the event that residents visit Star Mall. Then, we have

$P(A)=62\%$

$P(B)=73\%$

$P(A\cap B)=48\%$

We need to find the probability that a resident chosen at random shops at either Comet Mall or at Star Mall. It means, we have to find the value of $P(A\cup B)$.

We know that,

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

On substituting the given values, we get

$P(A\cup B)=62\%+73\%-48\%$

$P(A\cup B)=87\%$

Therefore, the probability that a resident chosen at random shops at either Comet Mall or at Star Mall is 87%.