Let $Y_i$ denote the number of packages brought by customer $i$ . If, for instance, $X=2$ customers are in line, then the total number of packages is $Y=Y_1+Y_2$ , and

$P(Y=y)=P(Y_1=y_1,Y_2=y_2)=P(Y_1=y_1)P(Y_2=y_2)$

since the number of packages brought by any customer is independent from the number of packages brought by any other.

a. $P(X=3,Y=3)$ is the probability that a total of 3 packages are waiting to get wrapped from among a total of 3 customers. This means each customer must have exactly one package. So

$P(X=3,Y=3)=P(X=3)P(Y=3)^3\approx0.0416$

b. $P(X=4,Y=11)$ is the probability that a total of 11 packages are brought by 4 customers. The only way for there to be 11 packages is if 3 customers bring 3 packages and the last 1 brings 2. There are $\dbinom43=4$ ways this can happen, so

$P(X=4,Y=11)=4P(X=4)P(Y=3)^3P(Y=2)\approx0.0002$

6 0

3 years ago

Suppose you're hiring a new worker for your business. You'd like someone reliable. Suppose you use administer a test to job-seek

stiks02 [169]

Answer:

You will have 21 positive results.

Step-by-step explanation:

Sensitivity of test:

Is the true positive rate, that is, the proportion of positive results that give positive tests.

Specificity of test:

True negative rate, that is, the proportion of negative results that give negative tests.

90% sensitive, 20 reliable people apply

0.9*20 = 18

95% specific, 60 unreliable people apply

1 - 0.95 = 0.05 of positive results.

0.05*60 = 3

How many positive results will you have?

18 + 3 = 21

You will have 21 positive results.

5 0

3 years ago

A recipe requires teaspoon of ground cinnamon, 1 teaspoon of ground

Ann [662]

Answer:

2 teaspoons of cinnamon 2 teaspoons of nutmeg and 2 teaspoons of allspice. which would be 6

Step-by-step explanation:

4 0

3 years ago