SOLUTION: i pick a random number from {1, 2, 3,⋯,10}, and call it N. Suppose that all outcomes are equally likely. Let A be the event that N is less than 7, and let B be the event that N i

Question 1177641: i pick a random number from {1, 2, 3,⋯,10}, and call it N. Suppose that all outcomes are equally likely. Let A be the event that N is less than 7, and let B be the event that N is an even number. Are A and B independent? Prove that
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
If independent
P(A and B)=P(A)*P(B)
even number < 7 has probability 3/10 (2,4,6)
P(A)=6/10
P(B)=1/2
their product is 3/10, so they are independent.
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Look at it this way: if you know the number is less than 7, between 1-6, do you have any other information about whether the number is even or odd? You do not, since 2 even numbers and two odd numbers were removed from the sample space.
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