Respuesta :
Answer: The required probabilities are
(a) 0, (b) 0.90, (c) 0.75, (d) 0.35, (e) 0.10 and (f) 0.25.
Step-by-step explanation: Given that A and B are two mutually exclusive events with P(A) = 0.25 and P(B) = 0.65.
We know that, for any two mutually exclusive events X and Y, we have
[tex]P(X\cap Y)=0.[/tex]
(a) Since A and B are mutually exclusive events, so
[tex]P(A\cap B)=0.[/tex]
(b) From Addition theorem of probability, we have
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.25+0.65-0=0.90.[/tex]
(c) We have
[tex]P(\bar{A})=1-P(A)=1-0.25=0.75.[/tex]
(d) We have
[tex]P(\bar{B})=1-P(B)=1-0.65=0.35.[/tex]
(e) We have
[tex]P(not(A\cup B))=1-P(A\cup B)=1-0.90=0.10.[/tex]
(f) We have
[tex]P(A\cap not~B)=P(A)-P(A\cap B)=0.25-0=0.25.[/tex]
Thus, the required probabilities are
(a) 0, (b) 0.90, (c) 0.75, (d) 0.35, (e) 0.10 and (f) 0.25.
Probabilities : A] 0 , B] 0.90 , C] 0.75 , D] 0.35 , E] 0.10 , F] 0.25
Mutually Exclusive : events are those two events, which can't happen at the same time. So, Probability (A and B) = 0
Following are the probabilities for these mutually exclusive events :
A] P(A and B) = 0, are events are mutually exclusive
B] P (A or B) = P (A) + P (B) - P (A and B) = 0.65 + 0.25 = 0.90
C] P (Not A) = 1 - P (A) = 1 - 0.25 = 0.75
D] P (Not B) = 1 - P (B) = 1 - 0.65 = 0.35
E] P { Not (A or B) } = 1 - P (A or B) = 1 - 0.90 = 0.10
F] P (A and not B) = P (A), as both are mutually exclusive = 0.25
To learn more about Probability, refer https://brainly.com/question/17136647?referrer=searchResults
