Question 1186068
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<pre>
Suppose events A and B are independent and

P(A) = 1/4
    
P(B) = 1/5

Find the probability. (Enter the probability as a fraction.)
   _____
 P(A ∩ B)  the line is above a and b only
</pre>~~~~~~~~~~~~~~~~~~~~~~~~



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution in the post by @CPhill is incorrect, 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;since he incorrectly reads/interprets the problem.



<pre>
The fact that  " the line is above A and B only "  means, that the question is about P({{{A^c}}} ∩ {{{B^c}}}),

where  {{{A^c}}} is the complement to A  and  {{{B^c}}} is the complement to B.


We have then  {{{P(A^c)}}} = 1 - 1/4 = 3/4  and  {{{P(B^c)}}} = 1 - 1/5 = 4/5.


Since events A and B are independent,  the events  {{{A^c}}}  and  {{{B^c}}}  are independent, too.

Therefore,  P({{{A^c}}} ∩ {{{B^c}}})}}} = {{{P(A^c)*P(B^c)}}} = {{{(3/4)*(4/5)}}} = {{{3/5}}}.    <U>ANSWER</U>
</pre>

Solved correctly.