Probability BUS201

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Probability
The probability that the first customer orders a dessert
The total number of customers that ordered a dessert was 136 and the total number of the customers in the restaurant at that period was 600, dividing the total number of customers by the number of customers that ordered a dessert gives probability of first customer to order a dessert.
136÷600= 0.22667
The probability that the first customer will order a dessert or has ordered beef entrée
Probability of first customer ordering dessert + Probability of first customer ordering beef entree
P ordered dessert=136/600=0.22667
P ordered beef entrée=187÷600=0.31167
0.22667+0.31167=0.62334
Probability that the first customer is a female and does not order a dessert
From table 1, total number of customers of both gender that were present in the restaurant was 600 out of these total only 240 females ordered a dessert, this implies that to get the probability of the first customer is a female and does not order a dessert you get total number of females who did not order for dessert divided by total of the both gender (Degroot,Morris H and Mark J,144).
240÷600 = 0.4
Probability that the first customer is a female or does not order a dessert
The probability is achieved by summing up the probability of being a female and that of no dessert. The probability of being a female is attained by dividing the total number of females which is 280, by the sum total of both gender which is 600.

280÷600 = 0.46667
While the probability of no dessert is achieved by dividing the number of females who did not order dessert which is 240 by the sum total of both gender that is 600.
240÷600 = 0.4
Summation of the two probabilities above gives probability of the first customer being a female and does not order a dessert.
0.4 + 0.46667 = 0.866
Suppose the first person from whom the waiter takes the dessert order is a female. What is the probability that she does not order dessert?
In this case tabulating probability of a female to order a dessert is calculated then divided by the possibility of a female not ordering a dessert. The probability of a customer being a female is equal to the number of females in the restaurant which in this case is 280 divided by the aggregate of customers which is 600.
280÷600=0.467
The probability of female not ordering a dessert is equal to number of females who have not ordered dessert divided by the total number of customers.
240÷600=0.4
Therefore the answer is 0.467+0.4=0.867
Are gender and ordering dessert independent?
According to (Ade and Peter Ar, 39), P (A/B) =P (A).
The probability of a customer not ordering a dessert and that of a female not ordering a dessert should be equal to the probability of a customer not ordering a dessert for gender and not ordering a dessert to be independent.
P (not ordering dessert/female not ordering a dessert) =P (not ordering dessert)
P customer not ordering dessert =464÷600=0.7733, P female not ordering dessert=0.867
0.7733÷0.867 =0.89193 instead of 0.7733 therefore ordering dessert and gender are dependent factors.
Is ordering a beef entree independent of whether the person orders dessert?
Using the formulae, P (A n B) =P (A) ×P (B) (Ade and Peter Ar, 40).
The probability of a customer to order beef entrée and a dessert should be equal to probability of a customer to order beef entrée multiplied by the probability of a customer to order a dessert for ordering a beef entrée to be independent of a customer ordering a dessert.
P (A n B) = 71÷600=0.1183
P (A) =187÷600=0.3117, P (B) = 136÷600=0.2267
P (A) × P (B) = 0.3117×0.2267=0.07066239
The answer to this question is no since P (A n B) which is 0.1183 is not equal to P (A) ×P (B) which is 0.07066239.
Below are some of the things to do to increase the probability of a customer to order dessert (Degroot,Morris H and Mark J,147).
• Reduce the price of the dessert.
• Providing a variety of desserts.

Works cited
DeGroot, Morris H., and Mark J. Schervish. Probability and statistics. Pearson Education, 2012.
Ade, Peter AR, et al. “Planck 2015 results-xiii. Cosmological parameters.” Astronomy & Astrophysics 594 (2016): A13.