Basic probability question: set theory

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WlND

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In North America, 98% of all people have a desktop computer. 49% of people have a laptop given that they have a desktop computer. How many people have a desktop computer and a laptop.


would that be 98+49-100= 47 % of people have a laptop

98+47-49=96

so 96% of people have a desktop and laptop computer?

Is that right?
 
WlND said:
In North America, 98% of all people have a desktop computer. 49% of people have a laptop given that they have a desktop computer. How many people have a desktop computer and a laptop.


would that be 98+49-100= 47 % of people have a laptop

98+47-49=96

so 96% of people have a desktop and laptop computer?

Is that right?
Click to expand...
P(desktop) = 0.98
P(laptop | desktop) = 0.49

Are you familiar with a Venn diagram, two intersecting circles in a box? The "desktop" circle covers 98% of the box. We don't know the total area of the "laptop" circle, but we do know that 49% of the "desktop" circle is also in the "laptop" circle. The question wants the intersection or the two circles:

P(desktop \(\displaystyle \cap\) laptop) = P(desktop) * P(laptop | desktop) = . . .
 
DrPhil said:
P(desktop) = 0.98
P(laptop | desktop) = 0.49

Are you familiar with a Venn diagram, two intersecting circles in a box? The "desktop" circle covers 98% of the box. We don't know the total area of the "laptop" circle, but we do know that 49% of the "desktop" circle is also in the "laptop" circle. The question wants the intersection or the two circles:

P(desktop \(\displaystyle \cap\) laptop) = P(desktop) * P(laptop | desktop) = . . .
Click to expand...


I am farmilar with the ven diagrams but the wording "49% of people have a laptop given that they have a desktop computer" sounded like it was the intersection of the 2 circles. Now that you point it out, however, I realize that they were referring to conditional probability. So the answer is just 0.98*0.49=0.482

thanks for your help
 
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