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givi [52]
2 years ago
15

How to solve this 2 question? ​

Mathematics
1 answer:
Tpy6a [65]2 years ago
6 0

8. For brevity, let U = unemployed, E = employed, M = male, F = female. We're given that

P(M) = P(F) = 50/100 = 1/2

P(U) = 60/100 = 3/5

P(M | U) = 2/3

P(E) = 40/100 = 2/5

P(F | E) = 3/4

8a. This follows immediately from the given information. Specifically,

P(E) = 1 - P(U) = 1 - 3/5 = 2/5

8b. By definition of conditional probability,

P(A | B) = P(A and B) / P(B)   ⇒   P(A and B) = P(A | B) P(B)

It follows that

P(M and U) = P(M | U) P(U) = 2/3 • 3/5 = 2/5

8c. Using Bayes' rule/the definition of conditional probability,

P(U | F) = P(U and F) / P(F) =  P(F | U) P(U) / P(F)

Since F and M are mutually exclusive,

P(F | U) = 1 - P(M | U)

and so

P(U | F) = (1 - 2/3) • 3/5 / [(1 - 2/3) • 3/5 + 3/4 • 2/5] = 2/5

8d. Here we assume gender and employment status are independent, so for instance

P(F and E) = P(F) P(E)

We then have by the inclusion/exclusion principle that

P(F or U) = P(F) + P(U) - P(F and U) = P(F) + P(U) - P(F) P(U)

We also have by the law of total probability

P(F) = P(F and U) + P(F and E)

so

P(F or U) = P(F and U) + P(F and E) + P(U) - P(F) P(U)

By the assumed independence,

P(F or U) = P(F) P(U) + P(F) P(E) + P(U) - P(F) P(U)

P(F or U) = P(F) P(E) + P(U)

P(F or U) = 1/2 • 2/5 + 3/5 = 4/5

9.

a. This is mostly a matter of counting the ways a given type of stamp can fall out.

P(A) = \dfrac{\dbinom{20}3}{\dbinom{24}3} = \dfrac{285}{506}

since there are 20 non-green stamps.

P(B) = \dfrac{\dbinom21 \dbinom{22}2}{\dbinom{24}3} = \dfrac{21}{92}

since there are 2 red and unused stamps, 1 of which we want; the other 2 stamps come from the remaining 22 non-red-and-unused stamps.

P(A \cap B) = \dfrac{\dbinom21 \dbinom{18}2}{\dbinom{24}3} = \dfrac{153}{1012}

since exactly 1 of the stamps must be red and unused, and the other 2 stamps that fall out can be neither green nor red and unused.

P(A \cup B) = P(A) + P(B) - P(A \cap B) = \dfrac{162}{253}

which follows from the inclusion/exclusion principle.

b. There is a total of 10 used stamps, so the probability of at least 1 going missing is

P(C) = \dfrac{\dbinom{10}1\dbinom{14}2 + \dbinom{10}2\dbinom{14}1 + \dbinom{10}3}{\dbinom{24}3} = \dfrac{415}{506}

By definition of conditional probability,

P(C \mid A) = \dfrac{P(C \cap A)}{P(A)}

However, there are no used green stamps; any used stamp that goes missing must be red, blue or yellow. So the event A ∩ C is really just the event C, and

P(C \mid A) = P(C) = \dfrac{415}{506}

c. A and C are independent if and only if

P(A \cap C) = P(A) P(C)

We know

P(C \cap A) = P(C)

so if A and C are independent, then

P(C) = P(A) P(C)

but this would imply P(A) = 1, which is clearly not the case as we found in 9.a. So A and C are not independent.

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Question 4
Elanso [62]

Answer:

a A = 30 + 0.45 n

b A = 90.3

c 0 customers

Step-by-step explanation:

Given

Base\ Amount = 30

Rate = 0.45 per customer

Solving (a): Amount (A) on n customers

This is calculated as:

A = Base\ Amount + Rate * n

A = 30 + 0.45 * n

A = 30 + 0.45 n

Solving (b): Amount on 134 customers

In this case: n = 134

So:

A = 30 + 0.45 * 134

A = 30 + 60.3

A = 90.3

Solving (c): Customers at noon.

At noon, the amount is 30.

So:

A = 30 + 0.45 n

30 = 30 + 0.45n

Collect like terms

0.45n = 30 - 30

0.45n =0

n = 0

6 0
3 years ago
Liza comes to the swimming pool once every 6 days. Jenny comes once every 4 days and Olga comes once every 10 days. This Monday
a_sh-v [17]

Answer:

Step-by-step explanation: 60 days

7 0
3 years ago
"let v = r 2 with the usual addition and scalar multiplication defined by k(u1, u2) = (ku1, 0). determine which of the five axio
expeople1 [14]
Let \mathbf u\in\mathbb R^2, where

\mathbf u=(u_1,u_2)

and let k\in\mathbb R be any real constant.

Given this definition of scalar multiplication, we can see right away that there is no identity element e such that

e\mathbf u=\mathbf u

because

e\mathbf u=e(u_1,u_2)=(eu_1,0)\neq(u_1,u_2)=\mathbf u
5 0
3 years ago
1. 267.935:39=<br><br><br> 2. 689.354:78=<br><br><br><br> 3. 96.873:56=
USPshnik [31]

​Question 1.) 267.935:39=

Answer 1.) 6.870 approximately​

Question 2.) 689.354:78​

Answer 2.) 8.838 approximately​

Question 3.) 96.873:56​

Answer 3.) 1.730 approximately​

Explanation : Since the numerators are expressed in thousandths, the answers must be expressed in thousandths too.​

​Hope this helps!​​​​

​\textit{\textbf{Spymore}}​​​​​​​

4 0
3 years ago
Please solve and show your work
yaroslaw [1]

Answer:

791.28

Step-by-step explanation:

1. 3.14*9²=254.34

2. 3.14*9*19=536.94

3. 536.94+254.34=791.28

5 0
2 years ago
Read 2 more answers
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