Need to know if my answer are correct or no ?

[zorro]

Question :
Suppose A and B are two events with P(A)=0.5 and P(A B)=0.8
i) For what value of P(B) would A and B be mutually exclusive
ii) For what value of P(B) would A and B be independent

Solution
i)
if P(A) = 0.5 and P(A B)=0.8 then

P(B) = P(A B) - P(A) = 0.8 - 0.5 = 0.3 _{(Is this correct ?)}

ii) _{NO clue on how to solve it}

[maggiemagnet]

Your first answer looks fine to me. For the second, what is the formula or rule for independent events?

[zorro]

The rule of independent events ,

But how do i use this as i dont know the value of

[Martingale]

Question :
Suppose A and B are two events with P(A)=0.5 and P(A B)=0.8
i) For what value of P(B) would A and B be mutually exclusive

As stated there is no answer to this question. if it was worded ...


i) For what value of P(B) could A and B be mutually exclusive

then your answer is correct

[Martingale]

The rule of independent events ,

But how do i use this as i dont know the value of

We also have

[zorro]

The rule of independent events ,

But how do i use this as i dont know the value of

We also have

How should i use this in solving the 2nd question

ii) For what value of P(B) would A and B be independent.

[Martingale]

The rule of independent events ,

But how do i use this as i dont know the value of

We also have

How should i use this in solving the 2nd question

ii) For what value of P(B) would A and B be independent.

we have two equations equal to the same thing




and




thus



replace the values you know and solve for

[zorro]

so

P(A) + P(B) - P(A B) = P(A). P(B)

0.5 + P(B) - 0.8 = 0.5 P(B)

P(B) - 0.3 = 0.5 P(B)

P(B) = 0.5/0.3 _{(Is this correct?)}

[Martingale]

so

P(A) + P(B) - P(A B) = P(A). P(B)

0.5 + P(B) - 0.8 = 0.5 P(B)

P(B) - 0.3 = 0.5 P(B)

P(B) = 0.5/0.3 _{(Is this correct?)}

How can P(B) = 0.5/0.3? That number is greater than 1!!

[zorro]

so

P(A) + P(B) - P(A B) = P(A). P(B)

0.5 + P(B) - 0.8 = 0.5 P(B)

P(B) - 0.3 = 0.5 P(B)

P(B) = 0.5/0.3 _{(Is this correct?)}

How can P(B) = 0.5/0.3? That number is greater than 1!!

from my work can u please point out the mistake