## Need to know if my answer are correct or no ?

Standard deviation, mean, variance, z-scores, t-tests, etc.

### Need to know if my answer are correct or no ?

Question :
Suppose A and B are two events with P(A)=0.5 and P(A $\cup$ 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 $\cup$ B)=0.8 then

P(B) = P(A $\cup$ B) - P(A) = 0.8 - 0.5 = 0.3 (Is this correct ?)

ii) NO clue on how to solve it

zorro

Posts: 28
Joined: Sat Jun 12, 2010 9:26 am

### Re: Need to know if my answer are correct or no ?

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

maggiemagnet

Posts: 294
Joined: Mon Dec 08, 2008 12:32 am

### Re: Need to know if my answer are correct or no ?

The rule of independent events $P(A \cap B) = P(A) . P(B)$,

But how do i use this as i dont know the value of $P(A \cap B)$

zorro

Posts: 28
Joined: Sat Jun 12, 2010 9:26 am

### Re: Need to know if my answer are correct or no ?

zorro wrote:Question :
Suppose A and B are two events with P(A)=0.5 and P(A $\cup$ 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

Martingale

Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

### Re: Need to know if my answer are correct or no ?

zorro wrote:The rule of independent events $P(A \cap B) = P(A) . P(B)$,

But how do i use this as i dont know the value of $P(A \cap B)$

We also have

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Martingale

Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

### Re: Need to know if my answer are correct or no ?

Martingale wrote:
zorro wrote:The rule of independent events $P(A \cap B) = P(A) . P(B)$,

But how do i use this as i dont know the value of $P(A \cap B)$

We also have

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

How should i use this in solving the 2nd question

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

zorro

Posts: 28
Joined: Sat Jun 12, 2010 9:26 am

### Re: Need to know if my answer are correct or no ?

zorro wrote:
Martingale wrote:
zorro wrote:The rule of independent events $P(A \cap B) = P(A) . P(B)$,

But how do i use this as i dont know the value of $P(A \cap B)$

We also have

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

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

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\Rightarrow P(A\cap B)=P(A)+P(B)-P(A\cup B)$

and

$P(A \cap B) = P(A)\cdot P(B)$

thus

$P(A)+P(B)-P(A\cup B)=P(A)\cdot P(B)$

replace the values you know and solve for $P(B)$

Martingale

Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

### Re: Need to know if my answer are correct or no ?

so

P(A) + P(B) - P(A $\cup$ 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?)

zorro

Posts: 28
Joined: Sat Jun 12, 2010 9:26 am

### Re: Need to know if my answer are correct or no ?

zorro wrote:so

P(A) + P(B) - P(A $\cup$ 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!!

Martingale

Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

### Re: Need to know if my answer are correct or no ?

Martingale wrote:
zorro wrote:so

P(A) + P(B) - P(A $\cup$ 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

zorro

Posts: 28
Joined: Sat Jun 12, 2010 9:26 am

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