A restaurant wants to examine the demand for entrees and desserts. It
recorded demand and gender of customers over two weeks. Entrees, mains
and desserts are ordered at the same time. INFO GIVEN:
GENDER = MALE = 96 ORDERED DESSERT, 224 DID NOT
GENDER = FEMALE = 40 ORDERED DESSERT, 240 DID NOT
CUSTOMERS WHO ORDERED DESSERT AND ENTREE = 71
CUSTOMERS WHO ORDERED DESSERT AND NO ENTREE = 65
CUSTOMERS WHO ORDERED ENTREE AND NO DESSERT = 116
CUSTOMERS WHO ORDERED NEITHER = 348

Q1.  A waiter approaches a table to take the order. What is the
probability that the first customer to order:
i) orders dessert
ii) orderes dessert and entree
iii) is female and does not order dessert?

Q2. Suppose the first person orders an entree. What is the probability
this person orders dessert?
Q3. Is ordering dessert independent of gender? Justify.
Q4. Are ordering dessert and ordering entree independent? If not,
would this be reasonable conclusion?

Hello curiousmaz!
These are my calculations to your excercises:

GENDER = MALE =   96 ORDERED DESSERT, 224 DID NOT  TOTAL: 320
GENDER = FEMALE = 40 ORDERED DESSERT, 240 DID NOT  TOTAL: 280
TOTAL             136                 464                 600

CUSTOMERS WHO ORDERED DESSERT AND ENTREE =    71
CUSTOMERS WHO ORDERED DESSERT AND NO ENTREE = 65
CUSTOMERS WHO ORDERED ENTREE AND NO DESSERT = 116
CUSTOMERS WHO ORDERED NEITHER =               348
TOTAL                                         600
CUSTOMERS WHO ORDERED DESSERT = 136
CUSTOMERS WHO ORDERED ENTREE =  187

Q1)
i) probability that the first customer orders dessert =
"all who order dessert" / "all customers" = 136/600 = 22.7%

ii) probability that the first customer orders dessert and entree =
"customers who order desert and entree" / "all customers" = 71/600 = 11.8%

iii) probability that the first customer is female and does not order dessert =
"female customers who didn't order dessert" / "all customers" = 240/600 = 40.0%

Q2) probability that a person who orders entree orders dessert =
"customers who ordered dessert and entree" / "customers who ordered entree" =
71/187 = 38.0%

Q3) "probability that a male orders dessert" =
"males who order dessert" / "all males" = 96/320 = 30.0%
"probability that a female orders dessert" =
"females who order dessert" / "all females" = 40/280 = 14.3%

conclusion: generally males order twice as often as women.
answer: ordering dessert is dependant of gender

Q4) "customer who orders dessert orders entree" =
"customer orders dessert and entree" / "customer orders dessert" = 71/136 =52.2%

"customer who orders dessert does not order entree" =
"customer orders dessert and no entree" / "customer orders dessert" =
65/136 = 47.8%

"customer who orders entree orders dessert" =
"customer orders entree and dessert" / "customer orders entree" =
71/187 = 38.0%

"customer who orders entree does not order dessert" =
"customer orders entree and no dessert" / "customer orders entree" =
116/187 = 85.3%

conclusion: it seems as ordering dessert does not change probability
of ordering entree, but ordering entree changes the probability of
ordering dessert

answer: only ordering dessert is dependant on ordering entree


Hope this gives you some idea about how to calculate probability. It's
not that difficult after all ;)

Quite simple really.

Hey thanks a million alikjunni. I had all but 2 of the calcs right, so
it has clarified some of the steps for me.
Thanks again.

The last calculation, for "customer who orders entree does not order
dessert", and the conclusion following it are incorrect. In fact the
conclusion cannot be correct for any set of data; if A affects B
(probabilistically speaking) then B affects A.

"customer who orders entree does not order dessert" = 116/187 as
stated, but this evaluates to 62.0%; as it must, since it is the
complementary probability to the previous one which was 38.0%.

Ordering dessert does indeed change the probability of ordering an
entree; by your own figures the overall probability of ordering an
entree is 187/600 = 31.7%, but among those who order dessert the
figure is 52.2%.

The problem is that you've changed methodology between Q3 and Q4. 8-)
In Q3 you correctly compared dessert rates for each gender. Similarly
for Q4 we want tom compare probability of ordering dessert for those
who do and do not order an entree. So compare "customer who orders
entree orders dessert", calculated by you as 38.0%, against "customer
who does not order entree orders dessert", 65/413 = 15.7%. Clearly
there is a difference here - customers who order entrees are about 2
1/2 times more likely to order desserts than those who do not.

Thanks, I spotted that error too when going over it again.