1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
777dan777 [17]
3 years ago
13

A restaurant needs a staff of 3 waiters and 2 chefs to be properly staffed. The joint probability model for the number of waiter

s (X) and chefs (Y) that show up on any given day is given below.
X
0 1 2 3
Y 0 K 0.02 0.01 0.03 1
1 0.01 0.03 0.05 0.04 2
2 0.02 0.01 0.04 0.69
A restaurant needs a staff of 3 waiters and 2 chef
a) What must the value of k be for this to be a valid probability model?
b) What is the probability that at least one waiter and at least one chef show up on any given day?
c) What is the probability that more chefs show up than waiters on any given day?
d) What is the probability that more than three total staff (waiters and chefs) will show up on any given day?
Mathematics
1 answer:
Zina [86]3 years ago
8 0

Answer:

a) The value of k that mass this a valid pribability model = 0.04

b) The probability that at least one waiter and at least one chef show up on any given day = 0.86

c) The probability that more chefs show up than waiters on any given day = 0.04

d) The probability that more than three total staff (waiters and chefs) will show up on any given day = 0.77

Step-by-step explanation:

The table of probabilities represents the combined probabilities of whatever number of waiters and chef.

The joint probability model for the number of waiters (X) and chefs (Y), including the 'total' row amd column, showing the sum of the joint probabilities along a row or column

Note That, for this to be a valid probability model, all of the joint probabilities must sum up to give 1.00

Y/X | 0 | 1 | 2 | 3 | Total

0 | K | 0.02 | 0.01 | 0.03 | (k+0.07)

1 | 0.01 | 0.03 | 0.05 | 0.04 | 0.13

2 | 0.02 | 0.01 | 0.04 | 0.69 | 0.76

T | (k+0.03) | 0.07 | 0.10 | 0.76 | 1.00

Note; (Y/X) just shows that Y is for the vertical and X takes the horizontal. And T = total along the vertical.

a) Using either the total along the vertical or horizontal, it should end up at the same answer of 1.00 if this is truly a valid probability model.

(k+0.07) + 0.13 + 0.76 = 1.00

or

(k+0.03) + 0.07 + 0.10 + 0.76 = 1.00

Either ways,

k = 1.00 - 0.96 = 0.04

The table then becomes

Y/X | 0 | 1 | 2 | 3 | Total

0 | 0.04 | 0.02 | 0.01 | 0.03 | 0.11

1 | 0.01 | 0.03 | 0.05 | 0.04 | 0.13

2 | 0.02 | 0.01 | 0.04 | 0.69 | 0.76

T | 0.07 | 0.07 | 0.10 | 0.76 | 1.00

b) Probability that at least one waiter and at least one chef show up on any given day = P(X≥1 n Y≥1)

This probability = P(X=1 n Y=1) + P(X=1 n Y=2) + P(X=2 n Y=1) + P(X=2 n Y=2) + P(X=3 n Y=1) + P(X=3 n Y=2)

= 0.03 + 0.01 + 0.05 + 0.04 + 0.04 + 0.69

= 0.86

c) Probability that more chefs show up than waiters on any given day = P(X n Y) where (Y > X)

This probability = P(X=0 n Y=1) + P(X=0 n Y=2) + P(X=1 n Y=2)

= 0.01 + 0.02 + 0.01

= 0.04

d) Probability that more than three total staff (waiters and chefs) will show up on any given day = P(X n Y) where (X + Y) > 3

This probability = P(X=2 n Y=2) + P(X=3 n Y=1) + P(X=3 n Y=2)

= 0.04 + 0.04 + 0.69

= 0.77

Hope this Helps!!!

You might be interested in
Andrew drove 45 more miles than Nicole. If they drove a combined total of 111 miles, how many miles did Nicole drive?
Airida [17]

Answer:

Nicole drove 66 miles.

Step-by-step explanation:

You can set of an equation of 45 - x = 111 x representing the amount of miles Nicole drove. You would subtract 45 from both 45 and 111 and get that x = 66.

8 0
3 years ago
Complete the table for the given rule y=1/3x i dont have a calculator
Licemer1 [7]

Do up one over 3 and start at 0, that is what I recommend

5 0
3 years ago
. Using the Binomial Theorem explicitly, give the 15th term in the expansion of (-2x + 1)^19
timofeeve [1]
Let's rewrite the binomial as:
(1 - 2x)^{19}

\text{Binomial expansion:} (1 + x)^{n} = \sum_{r = 0}^n\left(\begin{array}{ccc}n\\r\end{array}\right) (x)^{r}

Using the binomial expansion, we get:
\text{Binomial expansion: } (1 - 2x)^{19} = \sum_{r = 0}^{19}\left(\begin{array}{ccc}19\\r\end{array}\right) (-2x)^{r}

For the 15th term, we want the term where r is equal to 14, because of the fact that the first term starts when r = 0. Thus, for the 15th term, we need to include the 0th or the first term of the binomial expansion.

Thus, the fifteenth term is:
\text{Binomial expansion (15th term):} \left(\begin{array}{ccc}19\\14\end{array}\right) (-2x)^{14}
3 0
3 years ago
How many cubic feet in a 5 gallon bucket?
Rudiy27
5 gallons is 0.66 cubic feet, 0.5 cubic feet per container.
8 0
3 years ago
Read 2 more answers
Write the sum as a product of the GCF and a sum: 39 + 91
zysi [14]
13(3 + 7)

Hope I Helped You!!! :-)

Have A Good Day!!!
4 0
3 years ago
Other questions:
  • Does anyone know how to do 15 and 16?????
    14·2 answers
  • Check my answer. I think it C but i really don't know.
    6·2 answers
  • tinas salsa class membership which s $15 is deducted automatically from her bank account every month. which expression show the
    10·1 answer
  • Write to polynomial in standard form then name the polynomial based on its degree and number terms.
    15·1 answer
  • If m=3 = what is the value of 3m?​
    10·1 answer
  • 1. Four cards are drawn at random without replacement from a standard deck of 52 cards. Compute the probability that all are of
    14·1 answer
  • Guys please which one is the right answer
    6·2 answers
  • There are two spinners containing only white and green slices. Spinner A has 4 white slices and 1 green slice. All the slices ar
    7·1 answer
  • Ben the camel drinks tea (so classy!). He drinks 405 liters of tea every 2 days. How many liters of tea does Ben drink every 6 d
    5·1 answer
  • A baker has 20 pounds of sugar. He uses ⅜ of the sugar to bake cookies.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!