Simple beginners probability question

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January 15th 2011, 01:38 PM
greatsheelephant

Simple beginners probability question

Hi, could you check over my work to see if this is correct?

You are given $P(A \cup B)=0.7$ and $P(A \cup B\prime)=0.9$ . Determine P(A).

Find B:
$P(A \cup B\prime)=1-B=0.9 \\ B=0.1$

Then:
$P(A)=P(A\cup B)-P(B)=0.7-0.1 \\ =0.6$
January 15th 2011, 01:43 PM
dwsmith

Quote:

Originally Posted by greatsheelephant

Hi, could you check over my work to see if this is correct?

You are given $P(A \cup B)=0.7$ and $P(A \cup B\prime)=0.9$ . Determine P(A).

Find B:
$P(A \cup B\prime)=1-B=0.9 \\ B=0.1$

Then:
$P(A)=P(A\cup B)-P(B)=0.7-0.1 \\ =0.6$

$P(A)=P(A\cup B)-P(B)+P(A\cap B)$
January 15th 2011, 02:51 PM
Plato

From the given we get:
$P(A) + P(B) - P(A \cap B) = 0.7~\&$
$P(A) + P(B') - P(A \cap B') = 0.9$ .
Add those together.
Use these facts: $P(B)+P(B')=1~\&~ P(A \cap B) + P(A \cap B')=P(A)$ .
January 15th 2011, 03:50 PM
Soroban

Hello, greatsheelephant!

Quote:

$\text{Given: }\;P(A \cup B)\,=\,0.7,\;P(A \cup B')\,=\,0.9$
$\text{Determine }P(A).$

Using DeMorgan's Laws: . $\begin{Bmatrix} P(A \cup B) \:=\:0.7 & \Rightarrow & P(A' \cap B') \:=\: 0.3 \\ \\[-3mm]<br /> P(A \cup B') \:=\: 0.9 & \Rightarrow & P(A' \cap B) \:=\: 0.1 \end{Bmatrix}$

I used a Venn diagram:

Code:

*-------------------------------* | | | *---------------* | | |/A/////////////| | | |///////////////| | | |///////*-------+-------* | | |///////|///////| | | | |///////|///////| | | | |///////|///////| 0.1 | | | *-------+-------* | | | | B | | | 0.3 *---------------* | | | *-------------------------------*

Then it is evident that: . $P(A) \,=\,0.6$
January 19th 2011, 04:41 AM
greatsheelephant

Thank you! I came to 0.6 as well but I went about it by finding B, then subtracting the remaining union from the sample space, 1.