Question

In a clothing store, 55% of the customers buy a shirt, 25% of the customers

buy a pair of pants, and 20% of the customers buy both a shirt and a pair of
pants.
If a customer is chosen at random, what is the probability that he or she buys
a shirt or a pair of pants?
A. 0.225
B. 0.60
C. 0.30
D. 0.80

Answer 1

s= the customer buy a shirt

p= the customer buy pants

`p(s) = 0.55, p(p) = 0.25 , p(s \cap p) =0.20`

And we want to find this probability:

`p(s \cup p)`

And we can use the definition of total probability and we have:

`p(s \cup p) = p(s) +p(p) -p(s \cap p)`

And replacing we got:

`p(s \cup p) = 0.55+0.25 -0.20 = 0.60`

And the best answer for this case is:

B. 0.60

Explanation:

For this case we can define the following events:

s= the customer buy a shirt

p= the customer buy pants

And we have the following probabilities given:

`p(s) = 0.55, p(p) = 0.25 , p(s \cap p) =0.20`

And we want to find this probability:

`p(s \cup p)`

And we can use the definition of total probability and we have:

`p(s \cup p) = p(s) +p(p) -p(s \cap p)`

And replacing we got:

`p(s \cup p) = 0.55+0.25 -0.20 = 0.60`

And the best answer for this case is:

B. 0.60