Respuesta :
Answer:
(a) P (U and V) = 0.
(b) P (U|V) = 0.
(c) P (U or V) = 0.83.
Step-by-step explanation:
Mutually exclusive events are those events that cannot occur at the same time. That is, if events A and B are mutually exclusive then,
[tex]P (A\cap B) = 0[/tex]
Given:
Events U and V are mutually exclusive.
P (U) = 0.27 and P (V) = 0.56
(a)
As events U and V are mutually exclusive, the probability of their intersection will be 0.
That is,
[tex]P(U\ and\ V) = P (U\cap V) = 0[/tex]
Thus, the value of P (U and V) is 0.
(b)
The conditional probability of event B given A is:
[tex]P(B|A) =\frac{P(A\cap B)}{P(B)}[/tex]
Compute the value of P (U|V) as follows:
[tex]P(U|V) =\frac{P(U\cap V)}{P(V)}\\=\frac{0}{0.56}\\ =0[/tex]
Thus, the value of P (U|V) is 0.
(c)
The probability of the union of two events, say A and B, is
[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Compute the value of P (U or V) as follows:
[tex]P(U\ or\ V)=P(U\cup V)\\=P(U)+P(V)-P(U\cap V)\\=0.27+0.56-0\\=0.83[/tex]
Thus, the value of P (U or V) is 0.83.
The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.
Given :
- P(U) = 0.27
- P(V) = 0.56
- U and V are mutually exclusive events.
A) P(U and V)
P(U and V) = P(U [tex]\cap[/tex] V) = 0
Because U and V are mutually exclusive events.
B) P(U|V)
[tex]\rm P(U|V) = \dfrac{P(U\cap V)}{P(V)}[/tex]
[tex]\rm P(U|V) = \dfrac{0}{0.56}[/tex]
P(U|V) = 0
C) P(U or V)
[tex]\rm P(U \;or\;V) = P(U\cup V)[/tex]
[tex]\rm P(U \;or\;V) = P(U)+P(V)-P(U\cap V)[/tex]
P(U or V) = 0.27 + 0.56 - 0
P(U or V) = 0.83
The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.
For more information, refer to the link given below:
https://brainly.com/question/23017717
