Answer with Step-by-step explanation:
1.We are given that three events A, B and C.
P(A)=0.26
P(B)=0.5
P(C)=0.45
P(A/B)=0.26
P(B/C)=0
P(C/A)=0.26
When two events A and B are independent then
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]
If two events are mutually exclusive then
[tex]P(A\cap B)=0[/tex]
We know that [tex]P(A/B)=\frac{P(A\cap B)}{P(B)}[/tex]
[tex]P(A\cap B)=P(A/B)\times P(B)[/tex]
[tex]p(A\cap B)=0.26\times 0.5=0.13[/tex]
[tex]P(A)\times P(B)=0.26\times 0.5=0.13[/tex]
Hence, [tex]P(A\cap B)=P(A)\cdot P(B)[/tex]
Therefore, event A and B are independent.
[tex]P(B\cap C)=0\times 0.45=0[/tex]
Therefore, events B and C are mutually exclusive.
[tex]P(A\cap C)=0.26\times 0.26=0.0676[/tex]
[tex]P(A)\times P(C)=0.26\times 0.45=0.117[/tex]
[tex]P(A\cap C)\neq P(A)\cdot P(C)[/tex]
Hence, event A and C are neither independent nor mutually exclusive.
Answer: A and B are independent
B and C are mutually exclusive.
2.Let E be the event that randomly chosen person exercises and D be the event that a randomly chosen person is on a diet.
According to question
We have to find P(D/E).
Answer : P(D/E)
