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, 75% of the residents visit Star Mall, and 48% of the residents visit both malls.Use the formula P(A or B) = P(A) + P(B) - P(A and B).The probability that a resident chosen at random shops at either Comet Mall or at Star Mall is _______%.

Answer 1

Let's call event A the residents visiting Comet Mall, and event B the residents visiting Star Mall.

So the probability of event A is given by:

P(A) = 62% = 0.62

And the probability of event B is given by:

P(B) = 75% = 0.75.

The probability of event A and B, that is, a resident visiting both shops, is given by:

P(A and B) = 48% = 0.48

Now, calculating the probability of event A or B (that is, a resident visiting either Comet Mall or Star Mall), we have:

`\begin{gathered} P(\text{A or B)}=P(A)+P(B)-P(\text{A and B)} \\ P(\text{A or B)}=0.62+0.75-0.48 \\ P(\text{A or B)}=0.89 \end{gathered}`

So the probability wanted is 89%.