# Simple beginners probability question

• Jan 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 $\displaystyle P(A \cup B)=0.7$ and $\displaystyle P(A \cup B\prime)=0.9$. Determine P(A).

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

Then:
$\displaystyle P(A)=P(A\cup B)-P(B)=0.7-0.1 \\ =0.6$
• Jan 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 $\displaystyle P(A \cup B)=0.7$ and $\displaystyle P(A \cup B\prime)=0.9$. Determine P(A).

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

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

$\displaystyle P(A)=P(A\cup B)-P(B)+P(A\cap B)$
• Jan 15th 2011, 02:51 PM
Plato
From the given we get:
$\displaystyle P(A) + P(B) - P(A \cap B) = 0.7~\&$
$\displaystyle P(A) + P(B') - P(A \cap B') = 0.9$.
Use these facts: $\displaystyle P(B)+P(B')=1~\&~ P(A \cap B) + P(A \cap B')=P(A)$.
• Jan 15th 2011, 03:50 PM
Soroban
Hello, greatsheelephant!

Quote:

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

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

I used a Venn diagram:

Code:

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

Then it is evident that: .$\displaystyle P(A) \,=\,0.6$

• Jan 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.