Question

22% of the customers visiting the suit department of a certain store will purchase a suit, 30% will purchase a shirt and 28% will purchase a tie. 11% of customers purchase a shirt and a suit, 14% both a suit and a tie and 10% buy a shirt and a tie. Only 6% of customers buy all three items. Let A be the event that the customer purchases a suit, B the event that the customer purchases a shirt and C the event that the customer purchases a tie. If there are 1000 customers in the store one week, how many will purchase exactly one of these items

Answer 1

If there are 1000 customers in the store one week, how many will purchase exactly one of these items

1000 CUSTOMERS*28%=280

Explanation:

A The event that a persons buys a suit

B The event that a person buys a shirt

C The event that a person buys a tie

P(A)= 22%

P(B)= 30%

P(C)= 28%

P(AB)= 11%

P(AC)= 14%

P(BC)= 10%

P(ABC)= 6%

A u B u C Is the event that any item is bougth

AC u AC u BC Is the event that any two events occured

So the wanted probability is

P[(A u B u C )(AB u AC u BC)^c

P[(A u B u C )=P(AB)+ P(BC)+P(BC)

P[(A u B u C ) =0.22+0.30+0.28-0.11-0.14.-0.10+0.06

=0,51

0,51=+0,23+P[(A u B u C )(AB u AC u BC)^c

=0,28

1000 CUSTOMERS*28%=280