Question

Given P(A) = 0.7 and P(B) = 0.4 1) If A and B are independent events, compute P(A and B) - please center your answers in two decimal places 2) If P(A|B) = 0.1, compute P(A and B) ( THE ANSWERS ARE NOT 0.28 & 0.04 )

Answer #1

Given that

P(A) = 0.7 and

P(B) = 0.4

1 ) If A and B are independent events then we want to compute P( A and B)

i.e.

Given that, A and B are independent events then

...........( ANSWER)

========================================================================

2 ) Given that P(A/B) = 0.1

we want to compute P ( A and B ) i.e.

i.e.

i.e.

..........( ANSWER)

Suppose that the probability of A is 0.7 and the
probability of B is 0.4, and we know that the probability that both
A and B will occur is 0.28. Then the two events are

For two events A A and B B , P(A)=0.2 P(A)=0.2 and P(B)=0.4
P(B)=0.4 . (a) If A A and B B are independent, then P(A|B) P(A|B) =
= equation editor Equation Editor P(A∩B) P(A∩B) = = equation editor
Equation Editor P(A∪B) P(A∪B) = = equation editor Equation Editor
(b) If A A and B B are dependent and P(A|B)=0.1 P(A|B)=0.1 , then
P(B|A) P(B|A) = = equation editor Equation Editor P(A∩B) P(A∩B) = =
equation editor Equation Editor

1. Answer the following
a. If A and B are independent events, then P(A and B) =
P(A)P(B). True or false?
b. Let A, B and C be independent events with P(A) = 0.7, P(B) =
0.8, P(CC) = 0.5. Find P(A and B and C)
c. Compute the mean and standard deviation of the random
variable with the given discrete
probability distribution:
X P(X)
-3 0.10
0 0.17
1 0.56
3 0.17

1. A and B are independent events, and P(A) = 0.5 and P(B) =
0.8.
Find P(A and B)
2. Suppose that P(A) = 0.3, P(B) = 0.4, and
P(A and B) = 0.12.
a. What is P(A|B)?
b. What is P(B|A)?
c. Are A and B independent
3) Describe in your own words why the following statements
are
correct.
a. Two events cannot be independent if they are already
known to be mutually exclusive
b. Two events cannot be...

Let A and B be events with P (A)= 0.3 and P (B)=0.7, and P (A or
B)=0.9. (a) Compute . (b) Are and mutually exclusive? Explain. (c)
Are and independent? Explain.

Consider the following scenario:
• Let P(C) = 0.7
• Let P(D) = 0.4
• Let P(C|D) = 0.8
Q1. P(C AND D) =
Q2. Are C and D Mutually Exclusive?
Q3 Are C and D independent events?
Q4. P(D|C) =
Round your answer to two decimal places.

Two independent events A and B are given, and P(Bc|A ∪ B) = 1/3,
P (A|B) = 1/2. What is P (Bc)?

Let A and B represent events such that P(A) = 0.6, P(B) = 0.4,
and P(A ∪ B) = 0.76. Compute: (a) P(A ∩ B) (b) P(Ac ∪ B) (c) P(A ∩
Bc ) (d) Are events A and B mutually exclusive? Are they
independent? Explain by citing the definitions of mutual
exclusivity and independence.

a. Suppose that A and B are two events with P(A)=0.1, P(B)=0.2,
and P(A|B)=0.4. What is P(A ∪ B)? 10.
b. Suppose that F and G are two events with P(F)=0.1, P(G)=0.3,
and P(G|F)=0.5. What is P(F ∪ G)?

1，Let A and B be two events. Given that P(A)= 0.31, P(B)=0.72
and P(A and B)=0.18, the probability of P(\bar{A} and \bar{B}) is
（(please give your answer to two decimal
places).）
2，Recent data has shown that 40 percent of householders have a
Netflix subscription. If 20 households are randomly selected, the
probability that 5 of them have Netflix is Answer (please provide
your answer to 4 decimal places).

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