Question 1206319
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Answer: <font color=red size=4>0.17</font>


Work Shown
P(A) = P(A and S1) + P(A and S2)
P(A) = P(A given S1)*P(S1) + P(A given S2)*P(S2)
P(A) = 0.2*0.7 + 0.1*0.3
P(A) = 0.14 + 0.03
P(A) = <font color=red>0.17</font>
Event A has a 17% chance of happening.


In reference to tutor Theo's drawing, the left-most branch represents the P(A given S1)*P(S1) portion.
P(S1) is up top and P(A given S1) is the node underneath to the left.
The other branch that ends with "A" follows the pathway from S2 to A. 
That would be the P(A given S2)*P(S2) portion.


Here's another diagram we could make.
Draw a 10 by 10 square. Split it into two pieces labeled S1 and S2
*[illustration UploadedScreenshot_38.png]
S1 takes up 70% of the area
S2 takes up 30% of the area
P(S1) = 0.7
P(S2) = 0.3


Similar diagrams can be found <a href="https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1206322.html">here</a> and <a href="https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1206321.html">here</a>


Then we shade in the blue and red areas shown below.
The blue area is 20% of the area of S1 (i.e. the blue height is 20% of the height of the original square).
If we are certain to land in S1, then there is a 20% chance of landing in the blue area.
That leads to P(A given S1) = 0.20 = 20%
*[illustration UploadedScreenshot_39.png]
The red area is 10% of the area of S2
P(A given S2) = 0.10 = 10%
Either shaded region represents event A.


The blue region is 7 units across and 2 units tall.
There are 7*2 = 14 blue squares.
There are also 3*1 = 3 red squares
In all there are 14+3 = 17 squares shaded either blue or red.
This is out of 10*10 = 100 squares overall.
17/100 = <font color=red>0.17</font> is the answer we arrived at earlier.
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