Question

If we knew that P(A)=.4, P(A'∩ B')=.3, and P(A'∪B)=.75, then fine :

A. P(B)

B. (A∩B)

C.(AUB)

D. (A∩B' )

E. (AUB' )

F. (A' ∩B)

G.(A' UB)

Answer #1

Suppose that A and B are two events in a sample space
S with P(B)=0.04, P(A n B)=0.03 and P(A u B) =0.46
a) what is P(B) complement
b)what is P(A)
c)what is P( AUB) complement
d)what is P(A/B)
e)what is P(A complement n B)
f)Are two events A and B independent? justify your answer.
g) Are two events A and B mutually exclusive? Justify your
answer.

Suppose events A, B, and C are MUTUALLY INDEPENDENT and P(a) =
1/4, P(B) = 1/3, and P(C) =1/2 and N denotes the total number of
events among A, B, C, that occur
(a) Draw a venn diagram
(b) What is the E(N)
(c) What is E(N^2)
(d) What is Cov(Ia,N)
(e) Find P(N <= 2 | C)
Thank you!

Let A,B ∈ M3(R) with |A| = 4 and |B| = −3.
Evaluate (a) |AB|, (b) |5A|, (c) |BT|, (d) |A−1|, (e) |A3|, (f)
|ATA|, (g) |B−1AB|.

38. Let E and F be events with P(E) = .3, P(F) = .6, and P(E ∪
F) = .7. Find (a) P(E ∩ F) (b) P(E|F) (c) P(F|E) (d) P(Ec ∩ F) (e)
P(Ec |F)
answers: a. .2 b. .5 c. .67 d. .4 e. Please show work
how to get these answers and include venn diagram thank you

Suppose P(A) = 1/4 and P(B) = 2/5 .
(a) What is the maximum value of P(A ∩ B)?
(b) What is the minimum value of P(A ∩ B)?
(c) What is the maximum value of P(A ∩ B0 )
(d) What is the minimum value of P(A ∩ B0 )
(e) What is the maximum value of P(A ∪ B)?
(f) What is the minimum value of P(A ∪ B)?
(g) What is the maximum value of P(A|B)?
(h)...

1) P(A)=0.65, P(B)=0.37 and P(AUB)=0.65 a) Find P(A∩B).
b) Find P(B|A).
c) Are A and B independent, mutually exclusive, or dependent but
not mutually exclusive?

Let S = {a, b, c, d, e, f} with P(b) = 0.21, P(c) = 0.11, P(d) =
0.11, P(e) = 0.18, and P(f) = 0.19. Let E = {b, c, f} and F = {b,
d, e, f}. Find P(a), P(E), and P(F).

Suppose g: P → Q and f: Q → R where P = {1, 2, 3, 4},
Q = {a, b, c}, R = {2, 7, 10}, and f and g are defined by
f = {(a, 10), (b, 7), (c, 2)} and g = {(1, b), (2, a), (3, a), (4,
b)}.
(a) Is Function f and g invertible? If yes find f −1
and g −1 or if not why?
(b) Find f o g and g o...

7. Events A and B are independent. The P(A) = 3/5, P(not B) =
2/3. What is P(A and B)? a. 2/5 b. 1/5 c. 4/15 d. 2/15
8. A bag contains 4 red marbles, 3 blue marbles, and 7 green
marbles. If a marble is randomly selected from the bag, what is the
probability that it is blue? A) 1/11 B) 3/14 C) 1/7 D) 1/3
9. The distribution of the heights of students in a large class
is...

3) For a certain good we have q = f ( p ) = 200 e −
0.4 p.
a) Find the elasticity of demand at price p = $50.
b) At p = $50, is the demand elastic, inelastic, or
does it have unit elasticity? Explain what this means for this
product.
c) Find the elasticity of demand at price p = $20.
d) At p = $20, is the demand elastic, inelastic, or
does it have unit elasticity? Explain...

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